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[null,null,null,null,"angle of diameter ","φ","phi","ψ","psi hyp","tanψ",{"$f":"(BBB/AAA)^2/TAN(phi)","v":1.7503956233387994},"psi_ellipsi",{"$f":"-K1","v":-1.7503956233387994},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The tangent bisects ɅHPS",null,"ɅHPR",{"$f":"ASIN(AF2)","v":0.96737143084976118},"ɅRPS",{"$f":"ASIN(AH2)","v":0.96737143084976118},null,"F","STATHERA",{"$f":"ABSTCONST","v":40.99684400566349},null,null,"EPILOGI","GRAV RIGHT","REPULSIIVE","ELASTIC","GONIA",{"$f":"PI()/50*PERPATA","v":1.2566370614359172},"fi_1","fi_2","fi_3","PROS",{"$f":"IF(EPILOGI=1,1,-1)","v":-1},null,null,null,null,null,null,65,{"$f":"-BF1","v":-65},"VIMATA",8,"FI1",-0.9,-28,"kin energy","VELOCITY1","TAN","perp","perp1",null,null,null,null,"POT1x = MaSS * STATHera / Sqr((XP - cc) ^ 2 + YP ^ 2)",null,null,null,null,null,null,"VAPEIRO",{"$f":"VO*(AAA+CCC)/(BBB)","v":38.591260281974002},"VAPELXI",{"$f":"(CCC-AAA)*AAA/BBB","v":2.3321342537766014},"FOR ELASTIC FORCE",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(EPILOGI=1,$DU$2&$DU$3&$DU$4,\" \")","v":" "},null,null,null,null,null,null,"KEIMENO1",{"$f":"IF(EPILOGI=1,$DU$2&$DU$3&$DU$4,\" \")","v":" "},{"$f":"IF(EPILOGI=1,$DY$4&$DY$5,\"X\")","v":"X"},1,12,null,null,"KEIMENO2"]
[null,null,"AAA",null,null,10,{"$f":"RADIANS(F2)","v":0.17453292519943295},null,{"$f":"ATAN(K1)","v":1.0517475801609211},{"$f":"DEGREES(psi)","v":60.260697456318006},null,{"$f":"ATAN(M1)","v":-1.0517475801609211},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SO ɅHPR=ɅIPZ",null,15,"ang1",{"$f":"exoteriko(PX+CCC,PY,AF3,AG3)","v":0.82339693642029443},"ang2",{"$f":"exoteriko(AF3,AG3,PX-CCC,PY)","v":0.82339693642029443},"ABSTCPMST",{"$f":"1/2*(V_O^2=VO^2)*(1/(AAA-CCC)-1/(AAA+CCC))","v":0},"STATH2",7,"maza",null,1,{"$f":"IF(EPILOGI=1,TRUE,FALSE)","v":false},{"$f":"IF(EPILOGI=2,TRUE,FALSE)","v":true},{"$f":"IF(EPILOGI=3,TRUE,FALSE)","v":false},"FORCECONST",{"$f":"IF(EPILOGI=1,STATHERA,IF(EPILOGI=2,STATH22,STATH2))","v":-363.71923023977314},null,"POLLAPLASIASTIS",{"$f":"20","v":20},null,null,-12,-12,14,14,43,{"$f":"-BD2","v":-43},{"$f":"BE2*PI()/180","v":-0.75049157835756164},"Fi1=",{"$f":"BE2","v":-43},2,"X1Y1",{"$f":"xp","v":14.478532294194448},{"$f":"yp_","v":-6.3007910877516959},{"$f":"$CE$34","v":1101.5240482749964},{"$f":"SQRT(2*BM2/MASS)/SMIK","v":6.9969010545939279},{"$f":"tanfp","v":-0.70922567414383086},{"$f":"ATAN(BO4)","v":0.95390543332736},{"$f":"IF(vimata>0,xp,xp+1000)","v":14.478532294194448},{"$f":"IF(vimata>0,yp_,yp_+1000)","v":-6.3007910877516959},{"$f":"BQ3-BQ2","v":-1.2401960174414342},{"$f":"BN2*COS(BO3)","v":5.7072393909587396},{"$f":"BN2*SIN(BO3)","v":-4.0477207045529386},"POT2X = MaSS * STATHera / Sqr((XQ - cc) ^ 2 + YQ ^ 2)",null,null,null,null,null,null,"STATHAPOSI",{"$f":"CG6","v":67017.841656797886},"STATHELXI",{"$f":"CG5","v":302.15834320211923},"WE CAN ASSUME A STATHERA AND CALCULATE THE MAXIMUM DISTANCE",null,null,null,null,null,null,null,"KIN","POT",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"IN THE CASE OF atractive FORCE     FROM SIMILAR TRIANGLES AND PARALLELS:","so     ST'·V2=SP\"·V1=SR'·V3  Each product expresses the  law of areas for each point. ",1.5,5,null,null,-10,25]
[null,null,"BBB",null,null," ","Llhyp",{"$f":"COS(phi)^2/AAA^2-(SIN(phi)/BBB)^2","v":1.0767263655137353E-2},"LELLIPS",null,"LELIPS",{"$f":"COS(phi)^2/AAA^2+(SIN(phi)/BBB)^2","v":1.3179558823701018E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"LINE hps",null,null,{"$f":"1/SQRT(1+((BBB/AAA)^2*PX/PY)^2)","v":0.49605439724329736},{"$f":"AF3*(BBB/AAA)^2*PX/PY","v":0.86829144587263407},null,null,null,"STATH2",0.72,{"$f":"6^2/BBB^2","v":1.44},null,"PERPATA","STATH22",{"$f":"1/2*(V_OO^2-Voo^2)*(1/(AAA-CCC)-1/(AAA+CCC))","v":-363.71923023977314},null,"ENERGIA",null,null,null,null,null,null,-12,-12,12,12,24,{"$f":"BD3-25","v":-1},{"$f":"BE3*PI()/180","v":-1.7453292519943295E-2},"fi2",{"$f":"BE3","v":-1},2,"X2Y2",{"$f":"BK2+SIGN(BL2)*BN2*COS(BO3)","v":8.7712929032357074},{"$f":"BL2+(BO2)*(BK3-BK2)","v":-2.2530703831987564},"SIGNX",{"$f":"SIGN(BK3-BK2)","v":-1},{"$f":"ATAN(BO2)","v":-0.61689089346753656},{"$f":"ATAN(BO2)","v":-0.61689089346753656},{"$f":"IF(vimata>0,AX,AX+1000)","v":13.238336276753014},{"$f":"IF(vimata>0,AY,AY+1000)","v":-8.0494531323661764},{"$f":"(BQ3-BQ2)*(BK3-BK2)+(BR3-BR2)*(BL3-BL2)","v":0},{"$f":"1/BN2*1*COS(BP2)*ddd_2","v":2.4803920348828687},{"$f":"1/BN2*1*SIN(BP2)*ddd_2","v":3.4973240892289605},"POT3x = MaSS * STATHera / Sqr((XR - cc) ^ 2 + YR ^ 2)",null,null,null,null,null,null,"ENERGIAPS",{"$f":"1/2*MASS*VO^2+STATHAPOSI/(CCC+AAA)","v":3723.2134253776603},"ENERGELXI",{"$f":"1/2*MASS*VO^2-STATHELXI/(CCC-AAA)","v":16.786574622339828},"1/2MVO²+KA²=KSMAX²",null,null,"SMAX",{"$f":"SQRT(MASS/STATHAPOSI+AAA^2)","v":9.0000041448322854},null,{"$f":"AAA","v":9},"R",{"$f":"AAA","v":9},{"$f":"STATHELXI/CM3","v":33.573149244679911},{"$f":"ENERGELXI+CP3","v":50.359723867019738},{"$f":"SQRT(2*CQ3/MASS)","v":4.48819446401422},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ST/SD=SP:/P\"D=SP/(K/V1)=SP\"·V1/K     ST/SD=ST'/DT\"=ST'/(K/V2)=ST'·V2/K"," so  the law oa  areaas is valid for the case of the repulsive force",-1,10,null,null,-10,5]
[null,null,"CCC",null,null,null,"mhyp",{"$f":"COS(phi)*COS(psi)/AAA^2-SIN(phi)*SIN(psi)/BBB^2","v":0},null,null,null,{"$f":"COS(phi)*COS(psi_el)/AAA^2+SIN(phi)*SIN(psi_el)/BBB^2","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"-CCC","v":-10.295630140987001},0,null,{"$f":"AF3^2+AG3^2","v":1.0000000000000004},null,null,null,null,"mass_2",3,{"$f":"1/2*mass_2*6^2-1/2*STATH2*mass_2*AAA^2","v":-796.5},"PERPATA",20,"ENERGY",{"$f":"ENERGY_YP","v":408.21198777620447},null,"MAZA",null,null,null,null,null,null,-12,-12,10,10,36,{"$f":"BD4","v":36},{"$f":"BE4*PI()/180","v":0.62831853071795862},"fi3",{"$f":"BE4","v":36},null,"X3Y3",{"$f":"BK3+BQ5","v":8.8992388670419089},{"$f":"BL3+BR5","v":-2.6320556472205943},"SIGNY",{"$f":"SIGN(BL3-BL2)","v":1},{"$f":"TanpRpp","v":1.40998843732947},{"$f":"TAN(BP2)","v":1.40998843732947},"x","y",{"$f":"$CD$20","v":-8.0494531323661764},{"$f":"BT3*BT2","v":14.156191126503812},{"$f":"BU3*BU2","v":-14.156191126503813},null,null,null,null,null,"FOR ELASTIC",null,"SMAX²=MASS/STATH+AAA²",null,null,"from centripetal force = force",null,null,null,"XMAXELAST","QW",null,null,"foci",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SV/SE=SR'/ER\"=SR'/(K/V3)      SV/VE=ST/S'E=ST/T\"D=ST/T'V=ST·V2/K",null,null,null,"SV/SE=SR'/ER\"=SR'/(K/V3)      SV/VE=ST/S'E=ST/T\"D=ST/T'V=ST·V2/K"]
[null,null,null,null,null,null,"nhup",{"$f":"(COS(psi)/AAA)^2-(SIN(psi)/BBB)^2","v":-2.7119300596253046E-2},"NHYP",null,"NELIPS",{"$f":"COS(psi_el)^2/AAA^2+(SIN(psi_el)/BBB)^2","v":3.3195102201794065E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X²/A²-Y²/B²=1",null,{"$f":"PX","v":9.4907117906312095},{"$f":"PY","v":1.6734685548162302},null,null,null,null,"FOCI","HS","energy_3",{"$f":"1/2*mass_2*STATH2*AAA^2+1/2*mass_2*6^2","v":904.5},{"$f":"STATHERA","v":40.99684400566349},"Voo",2,"ENERGY_YP",{"$f":"1/2*MASS*VO^2-MASS*ABS(STATHERA)/(AAA-CCC)","v":408.21198777620447},null,"POT_ENERGY",null,null,124,"perpataa",{"$f":"AV5-90","v":34},null,-12,-12,7,7,3,null,{"$f":"IF(EPILOGI=1,\"ATTRACTIVE\",IF(EPILOGI=2,\"REPULSIVE\",\"ELASTIC\"))","v":"REPULSIVE"},null,null,null,"X4Y4",{"$f":"BK3+BQ6","v":9.171266785341313},{"$f":"BL3+BR6","v":-2.2484994277876282},"F",{"$f":"-BO3","v":0.61689089346753656},{"$f":"-BN3*DAA*COS(PI()/5)","v":0.32360679774997902},{"$f":"-BN4*DAA*SIN(PI()/5)","v":-0.23511410091698925},{"$f":"BO5*COS(BN5)+BP5*SIN(BN5)","v":0.1279459638062021},{"$f":"-BO5*SIN(BN5)+BP5*COS(BN5)","v":-0.37898526402183774},null,null,null,{"$f":"ddd_2","v":30},null,null,null,null,null,null,"SMAX²=X²+(B/A)²X²-B²",null,null,"epilogi =1",{"$f":"MASS*VO^2*(CCC-AAA)^2/aktin","v":302.15834320211923},null,null,"YMAXELAST",null,null,null,{"$f":"-CCC","v":-10.295630140987001},0,null,null,null,null,null,0,0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"IN THE CASE OF REPULSIVE FORCE      FROM SIMILAR TRIANGLES AND PARALLELS:",null,null,null,"so     ST'·V2=SP\"·V1=SR'·V3  SO S IS THE CENTER"]
[null,null,null,{"$f":"AAA*TAN(A10)","v":-286.3846435839647},{"$f":"BBB/COS(A10)","v":159.18112604548759},null,"Ahyp",{"$f":"1/SQRT(Llhyp)","v":9.6371213179447413},{"$f":"-15","v":-15},{"$f":"I6*SIN(phi)","v":-2.6047226650039548},null,0,{"$f":"\"MHNYMA\"&TEXT(L6,\"0\")","v":"MHNYMA0"},"Let CA, CB be the semi-axes of the hyperbola",null,null,null,null,null,-1,2,12,10,null,null,null,null,null,{"$f":"CCC","v":10.295630140987001},0,"F~QR/t²","t~QT∙SP","F~QR/(QT∙SP}²",null,{"$f":"-CCC","v":-10.295630140987001},0,"ddd_2_2",30,null,"V_OO",{"$f":"Voo*((AAA+CCC)/(AAA-CCC))","v":-29.78570740302127},null,{"$f":"1/2*MASS*VO^2","v":250},null,"KIN_ENERGY",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RADIANS(-27)","v":-0.47123889803846897},null,"X5Y5",{"$f":"BK3","v":8.7712929032357074},{"$f":"BL3","v":-2.2530703831987564},{"$f":"BK1","v":-0.9},null,{"$f":"BO5","v":0.32360679774997902},{"$f":"-BP5","v":0.23511410091698925},{"$f":"BO6*COS(BN5)+BP6*SIN(BN5)","v":0.39997388210560642},{"$f":"-BO6*SIN(BN5)+BP6*COS(BN5)","v":4.5709554111280915E-3},null,null,null,{"$f":"EPILOGI","v":2},null,null,{"$f":"ENERGIAPS","v":3723.2134253776603},null,null,null,"XMAX","=(SMAX²+B²)*A²/C²",null,"epilogi =2",{"$f":"MASS*VO^2*(CCC+AAA)^2/aktin","v":67017.841656797886},null,null,"ENERELAST",{"$f":"1/2*MASS*VO^2-1/2*STATHEL*AAA^2","v":-560},null,null,{"$f":"CCC","v":10.295630140987001},0,null,null,"elastic",null,null,0,0,null,null,"repulsion",null,{"$f":"ENERGIAPS","v":3723.2134253776603},{"$f":"STATHAPOSI","v":67017.841656797886},null,null,null,null,null,null,null,"attractive",null,null,null,null,null,null,null,null,null,null,"ST/TD=SP:/pD=SP/(K/V1)=SP\"·V1/K ST/TD=ST'/DT'=ST/(K/V2)=ST'·V2/K","so             ST'·V2=SP\"·V1=SR'·V3 "]
["ELLIPSE",null,null,{"$f":"AAA*TAN(-A10)","v":286.3846435839647},{"$f":"BBB/COS(-A10)","v":159.18112604548759},null,"BHYP",{"$f":"1/SQRT(-nhup)","v":6.0724053962811952},{"$f":"15","v":15},{"$f":"I7*SIN(phi)","v":2.6047226650039548},null,{"$f":"L6+1","v":1},{"$f":"\"MHNYMA\"&TEXT(L7,\"0\")","v":"MHNYMA1"},"PG, KD other conjugate diameters",null,null,null,null,null,-17,2,-7,-6,null,null,null,"X1 ",{"$f":"-Ahyp","v":-9.6371213179447413},"POINT WHERE THE ONE DIAMETER CUTS THE HYPERBBLA",null,"GV∙PV/QV²",{"$f":"SQRT((GX-VX)^2+(GY-VY)^2)*SQRT((PX-VX)^2+(PY-VY)^2)/((qx-VX)^2+(qy-VY)^2)","v":{"$error":"#NUM!"}},null,null,{"$f":"CCC","v":10.295630140987001},0,"AAA",{"$f":"AAA","v":9},null,"VO ",{"$f":"10","v":10},"V_O",{"$f":"VO*(AAA-CCC)/(AAA+CCC)","v":-0.67146298489359801},null,"VELOCITY",null,null,null,null,null,null,null,{"$f":"CCC","v":10.295630140987001},{"$f":"INT(2.4*BBB)","v":12},{"$f":"DEGREES(perpataa*PI()/180)","v":34},null,"angle of moving point= ",null,{"$f":"BF7-20","v":-20},{"$f":"PI()+BH6","v":2.6703537555513241},null,"FI2",0.2,-28,"kin energy","VELOCITY1","TAN","perp","perp1",null,null,null,null,{"$f":"PROS","v":-1},null,null,{"$f":"ENERGELXI","v":16.786574622339828},null,null,null,"1/2MVO²+1/2KR²=1/2KS²",null,null,"epilogi=3",{"$f":"MASS*VO^2/(AAA)/aktin","v":20},null,null,"STATHEL",{"$f":"CG7","v":20},null,null,"case of elastic force",null,null,null,null,{"$f":"ENERELAST","v":-560},null,null,null,null,"case of repulsive force with center at -c",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"case of attractive fore",null,null,null,"SV/VE=SR'/ER\"=SR'/(K/V3)     SV/VE=ST/V'E=ST/T\"D=ST/T'V=ST·V2/K",".Each product expresses the  law of areas for each points.  so  the law oa  areaas is valid for the case of the repulsive force\n"]
["FI",null,"MAXDX",{"$f":"ABS(D7-D6)","v":572.76928716792941},null,null,null,"                ",{"$f":"-20","v":-20},{"$f":"TAN(psi)*I8","v":-35.007912466775977},null,{"$f":"L7+1","v":2},{"$f":"\"MHNYMA\"&TEXT(L8,\"0\")","v":"MHNYMA2"}," PF a perpendicular to the diameter KD   Qv an ordinate to the diameter GP",null,null,null,null,null,null,null,7,9,8,5,null,"Y1",0,"GP",null,"QV²/QX²",{"$f":"((qx-VX)^2+(qy-VY)^2)/((qx-XX)^2+(qy-XY)^2)","v":{"$error":"#NUM!"}},"L/GV",{"$f":"L/SQRT((GX-VX)^2+(GY-VY)^2)","v":{"$error":"#NUM!"}},"PV/GV",{"$f":"SQRT((PX-VX)^2+(PY-VY)^2)/SQRT((GX-VX)^2+(GY-VY)^2)","v":{"$error":"#NUM!"}},"VELOCITY",null,null,"MASS",5,1,{"$f":"1/2*(V_O^2-VO^2)*(1/(AAA-CCC)-1/(AAA+CCC))","v":40.99684400566349},null,"energy22",{"$f":"1/2*MASS*Voo^2-STATH22*MASS/(AAA+CCC)","v":104.24911951104811},null,null,null,null,null,null,{"$f":"CCC","v":10.295630140987001},{"$f":"BB7","v":12},null,null,{"$f":"BE7& TEXT(BC7,\"0,0\")","v":"angle of moving point= 34"},null,null,null,null,"X1Y1",{"$f":"AAA/COS(BK7)","v":9.1830496044707335},{"$f":"BBB*TAN(BK7)","v":1.0135501775433626},{"$f":"$CE$35","v":287.28756608210824},{"$f":"SQRT(2*BM8/MASS)/SMIK","v":3.5732808832102632},{"$f":"taNFq","v":2.7963830820401911},{"$f":"ATAN(BO10)","v":-0.34343356328947983},{"$f":"BK8","v":9.1830496044707335},{"$f":"BL8","v":1.0135501775433626},{"$f":"BQ9-BQ8","v":-3.9526870079063414},{"$f":"BN8*COS(BO9)","v":1.2032027421992932},{"$f":"BN8*SIN(BO9)","v":3.3646157925504685},null,null,null,{"$f":"ENERELAST","v":-560},null,null,null,"S=SQRT(m/Kvo²+a²)",null,null,null,null,{"$f":"CCC","v":10.295630140987001},null,{"$f":"CH8^2","v":106.00000000000001},null,null,"c",null,"x","y","pot","kin",null,"f","vx","vy",null,null,"x","y","pot","kin",null,"f","vx","vy","L",null,"x","y","pot","kin",null,"f","vx","vy","L",null,null,null," ",null,null,null,null,null,"KEIMENO1"]
[{"$f":"-PI()/2","v":-1.5707963267948966},{"$f":"AAA*COS(A9)","v":5.51316804708879E-16},{"$f":"BBB*SIN(A9)","v":-5},null,null,"conjhyp",null,null,{"$f":"20","v":20},{"$f":"TAN(psi)*I9","v":35.007912466775977},null,3,"MHNYMA3","ZR the velocity at P",null,null,{"$f":"rx","v":8.0907117906312092},9,{"$f":"ry","v":-0.7770853178580881},0.5,null,null,null,null,null,null,"GX",{"$f":"AB7*COS(phi)","v":-9.4907117906312095},{"$f":"-AB9","v":9.4907117906312095},"PX","PC²/CD²",{"$f":"((PX)^2+PY^2)/(DX^2+DY^2)","v":2.51868083339017},"GV∙PV=",{"$f":"SQRT((GX-VX)^2+(GY-VY)^2)*SQRT((PX-VX)^2+(PY-VY)^2)","v":{"$error":"#NUM!"}},"line ","HI","FIND I AS CUT OF LINE SP AND LINE HI // TO DK",null,null,null,null,"IX","IY",{"$f":"1/(AAA-CCC)","v":-0.77182520563947976},null,null,null,null,null,null,null,null,"VIMATA = ",10,0,null,"s='STEP = '&",null,null,"CONJUGATE DIAMETERS",null,"X2Y2",{"$f":"BK8+SIGN(BL8)*BN8*COS(BO9)","v":10.386252346670027},{"$f":"BL8+(BO8)*(BK9-BK8)","v":4.378165970093832},"SIGNX",{"$f":"SIGN(BK9-BK8)","v":1},{"$f":"ATAN(BO8)","v":1.2273627635054167},{"$f":"ATAN(BO8)","v":1.2273627635054167},{"$f":"IF(vimata>0,$CB$21,BQ8)","v":5.2303625965643921},{"$f":"IF(vimata>0,BR8+TAN(BP8)*(BQ9-BQ8),BR8)","v":2.4270500064089169},{"$f":"(BQ9-BQ8)*(BK9-BK8)+(BR9-BR8)*(BL9-BL8)","v":0},{"$f":"1/BN8*1*COS(BP8)*ddd_2","v":7.9053740158126828},{"$f":"1/BN8*1*SIN(BP8)*ddd_2","v":-2.8269996577311081},null,null,null,{"$f":"1/2*STATHAPOSI*SMAX^2","v":2714225.087100314},null,null,null,{"$f":"1/2*MASS*VAPEIRO^2","v":3723.2134253776603},null,null,"EPILOGI",{"$f":"EPILOGI","v":2},{"$f":"AAA","v":9},{"$f":"BBB","v":5},null,null,null,null,{"$f":"1","v":1},{"$f":"CN9*AAA","v":9},{"$f":"BBB*SQRT(CO9^2/AAA^2-1)","v":0},{"$f":"-STATHEL*((CO9)^2+CP9^2)/2","v":-810},{"$f":"ENERELAST-CQ9","v":250},{"$f":"SQRT(2*CR9/MASS)","v":10},{"$f":"PI()/2","v":1.5707963267948966},{"$f":"$CS9*COS($CT9)","v":6.1257422745431001E-16},{"$f":"SIN($CT9)*$CS9","v":10},{"$f":"($CO9)*$CV9-$CP9*$CU9","v":90},{"$f":"1","v":1},{"$f":"CX9*AAA","v":9},{"$f":"BBB*SQRT(CY9^2/AAA^2-1)","v":0},{"$f":"STATHAPOSI/SQRT((CY9+CCC)^2+CZ9^2)","v":3473.2134253776603},{"$f":"ENERGIAPS-DA9","v":250},{"$f":"SQRT(2*DB9/MASS)","v":10},{"$f":"PI()/2","v":1.5707963267948966},{"$f":"DC9*COS(DD9)","v":6.1257422745431001E-16},{"$f":"SIN(DD9)*DC9","v":10},{"$f":"(CY9+CCC)*DF9-CZ9*DE9","v":192.95630140987001},{"$f":"1","v":1},{"$f":"DH9*AAA","v":9},{"$f":"BBB*SQRT(DI9^2/AAA^2-1)","v":0},{"$f":"STATHELXI/SQRT((DI9-CCC)^2+DJ9^2)","v":233.21342537766017},{"$f":"ENERGELXI+DK9","v":250},{"$f":"SQRT(2*DL9/MASS)","v":10},{"$f":"PI()/2","v":1.5707963267948966},{"$f":"DM9*COS(DN9)","v":6.1257422745431001E-16},{"$f":"SIN(DN9)*DM9","v":10},{"$f":"(DI9-CCC)*DP9-DJ9*DO9","v":-12.956301409870008},null,null,"KEIMENO2",{"$f":"IF(EPILOGI=2, $DU$5 & $DU$6&$DU$7,\"Z\")","v":"IN THE CASE OF REPULSIVE FORCE      FROM SIMILAR TRIANGLES AND PARALLELS:ST/TD=SP:/pD=SP/(K/V1)=SP\"·V1/K ST/TD=ST'/DT'=ST/(K/V2)=ST'·V2/KSV/VE=SR'/ER\"=SR'/(K/V3)     SV/VE=ST/V'E=ST/T\"D=ST/T'V=ST·V2/K"},{"$f":"IF(EPILOGI=2,$DV$6&$DV$7,\"Z\")","v":"so             ST'·V2=SP\"·V1=SR'·V3 .Each product expresses the  law of areas for each points.  so  the law oa  areaas is valid for the case of the repulsive force\n"},-1,-7,null,null,-20,-8]
[{"$f":"A9+PI()/100","v":-1.5393804002589986},0.28269683170315557,-4.9975328018286582,null,null,null,null,null,{"$f":"-PI()","v":-3.1415926535897931},{"$f":"10*COS($I10)","v":-10},{"$f":"10*SIN($I10)","v":-1.22514845490862E-15},4,"MHNYMA4","RQ the deviation due to the force",null,null,null,{"$f":"qx","v":{"$error":"#NUM!"}},10,{"$f":"qy","v":{"$error":"#NUM!"}},{"$f":"qy-1","v":{"$error":"#NUM!"}},null,null,null,null,null,"GY",{"$f":"AB7*SIN(phi)","v":-1.6734685548162302},{"$f":"-AB10","v":1.6734685548162302},"PY","EP²/PF²",{"$f":"((EX-PX)^2+(EY-PY)^2)/((PX-fx)^2+(PY-fy)^2)","v":1.4749642918713988},"PV∙L=",{"$f":"L*SQRT((PX-VX)^2+(PY-VY)^2)","v":{"$error":"#NUM!"}},"Y=TANSP*(X-CCC)",null,"TANSP*(X-CCC)=TAN(PSI)*(X+CCC)",null,null,null,null,{"$f":"CCC*(TANSP+TAN(psi))/(TANSP-TAN(psi))","v":0.88361084154276071},{"$f":"TAN(psi)*(AP10+CCC)","v":19.568094488069828},{"$f":"1/(AAA+CCC)","v":5.182520563948001E-2},null,null,null,null,null,null,null,null,{"$f":"CCC","v":10.295630140987001},{"$f":"2*BBB","v":10},{"$f":"BA9&TEXT(vimata,\"0\")","v":"VIMATA = 8"},null,"SMIK",3,null,"A",9,"X3Y3",{"$f":"BK9+BQ11","v":10.49867116950508},{"$f":"BL9+BR11","v":3.9942883746647935},"SIGNY",{"$f":"SIGN(BL9-BL8)","v":1},{"$f":"taNprpQ","v":-0.35760479543111018},{"$f":"TAN(BP8)","v":-0.35760479543111018},"x","y",null,{"$f":"BT9*BT8","v":9.5117676939368589},{"$f":"BU9*BU8","v":-9.5117676939368554},null,null,null,null,null,null,"aktin",{"$f":"BBB^2/AAA","v":2.7777777777777777},null,null,{"$f":"1/2*MASS*VAPEIRO^2","v":3723.2134253776603},null,{"$f":"CH9^2","v":81},{"$f":"CI9^2","v":25},{"$f":"CI10+CH10","v":106},null,null,null,{"$f":"CN9+0.5","v":1.5},13.5,5.5901699437494745,-2135,1575,25.099800796022265,{"$f":"ATAN(BBB^2*$CO10/(AAA^2*$CP10))","v":0.6405223126794245},{"$f":"$CS10*COS($CT10)","v":20.124611797498108},{"$f":"SIN($CT10)*$CS10","v":14.999999999999998},{"$f":"($CO10)*$CV10-$CP10*$CU10","v":89.999999999999957},{"$f":"CX9+0.5","v":1.5},13.5,5.5901699437494745,2741.7510533793825,981.46237199827783,19.813756554457591,{"$f":"ATAN(BBB^2*$CO10/(AAA^2*$CP10))","v":0.6405223126794245},{"$f":"DC10*COS(DD10)","v":15.886347551084324},{"$f":"SIN(DD10)*DC10","v":11.840984346137287},192.95630140987004,{"$f":"DH9+0.5","v":1.5},13.5,5.5901699437494745,46.893910522239509,63.680485144579336,5.0469985196977953,{"$f":"ATAN(BBB^2*$CO10/(AAA^2*$CP10))","v":0.6405223126794245},{"$f":"DM10*COS(DN10)","v":4.0466012769138011},{"$f":"SIN(DN10)*DM10","v":3.0161585110055693},-12.956301409870003,null,null,null,null,null,-1,-9,null,null,-20,-11]
[{"$f":"A10+PI()/100","v":-1.5079644737231006},0.56511467576382168,-4.990133642141358,{"$f":"IF(ABS(COS(A11))>0.0000000001,AAA/COS(A11),D10)","v":143.33373998917756},null,null,{"$f":"IF(ABS(COS($A11))>0.0001,BBB/COS(A11),G10)","v":79.62985554954308},null,{"$f":"I10+PI()/60","v":-3.0892327760299634},{"$f":"10*COS($I11)","v":-9.9862953475457381},{"$f":"10*SIN($I11)","v":-0.52335956242943804},5,{"$f":"\"MHNYMA\"&TEXT(L11,\"0\")","v":"MHNYMA5"},"Draw SP cutting the diameter DK in E, and the ordinate Qv in xand complete the parallelogram QRPx.",null,null,null,null,null,null,null,null,null,null,{"$f":"CCC+2","v":12.295630140987001},1,-6,-7,null,null,"QV²/QT²",{"$f":"((qx-VX)^2+(qy-VY)^2)/((qx-tx)^2+(qy-ty)^2)","v":{"$error":"#NUM!"}},"AC/PC",{"$f":"AAA/SQRT((PX)^2+(PY)^2)","v":0.93388883496170239},"Y=TAN(PSI)*(X+CCC)",null,"X(TANSP-TAN(PSI))=CCC*(TANSP+TAN(PSI))",null,null,null,null,{"$f":"-CCC","v":-10.295630140987001},0,null,null,null,null,null,null,null,null,null,{"$f":"CCC","v":10.295630140987001},{"$f":"BB10","v":10},null,null,null,null,null,"B",5,"X4Y4",{"$f":"BK9+BQ12","v":10.055902384821183},{"$f":"BL9+BR12","v":4.1526246153349602},"F",{"$f":"-BO9","v":-1.2273627635054167},{"$f":"-BN9*DAA*COS(PI()/5)","v":-0.32360679774997902},{"$f":"-BN10*DAA*SIN(PI()/5)","v":-0.23511410091698925},{"$f":"BO11*COS(BN11)+BP11*SIN(BN11)","v":0.112418822835054},{"$f":"-BO11*SIN(BN11)+BP11*COS(BN11)","v":-0.38387759542903876},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"CN10+0.5","v":2},18,8.6602540378443855,-3990,3430,37.040518354904272,0.57037681003940033,31.176914536239792,20.000000000000004,90.000000000000057,{"$f":"CX10+0.5","v":2},18,8.6602540378443855,2264.7849742859007,1458.4284510917596,24.153082214009537,0.57037681003940033,20.329590767545156,13.041438557952365,192.95630140987012,{"$f":"DH10+0.5","v":2},18,8.6602540378443855,26.067773119719941,42.854347742059772,4.1402583369668982,0.57037681003940033,3.4848454088245946,2.2355293720767908,-12.95630140986998]
[{"$f":"A11+PI()/100","v":-1.4765485471872026},0.84697481986663059,-4.9778098230154004,95.63448416654785,{"$f":"IF(ABS(COS(A12))>0.0000000001,BBB*TAN(A12),E11)","v":-52.894474967028067},{"$f":"IF(ABS(COS(A12))>0.001,AAA*TAN(A12),F11)","v":-95.210054940650522},53.130268981415476,null,{"$f":"I11+PI()/60","v":-3.0368728984701336},-9.9452189536827333,-1.0452846326765328,6,"MHNYMA6","EP =a because the tangent ZR is bisector of the angle HPS and so angle IPZ=angle RPS= angle HPR",null,null,null,null,null,null,null,null,null,null,null,null,"FIND THE CUT OF THE OTHER DIAMETER WITH THE RED HYPERBOLA",null,null,null,"QX²/QT²",{"$f":"((qx-XX)^2+(qy-XY)^2)/((qx-tx)^2+(qy-ty)^2)","v":{"$error":"#NUM!"}},"PE/PC",{"$f":"SQRT((PX-EX)^2+(PY-EY)^2)/SQRT((PX)^2+(PY)^2)","v":0.93388883496170216},"FIND DK",null,null,null,null,null,null,"IH",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C ",{"$f":"SQRT(AAA^2+BBB^2)","v":10.295630140987001},"X5Y5",{"$f":"BK9","v":10.386252346670027},{"$f":"BL9","v":4.378165970093832},{"$f":"BK7","v":0.2},null,{"$f":"BO11","v":-0.32360679774997902},{"$f":"-BP11","v":0.23511410091698925},{"$f":"BO12*COS(BN11)+BP12*SIN(BN11)","v":-0.33034996184884385},{"$f":"-BO12*SIN(BN11)+BP12*COS(BN11)","v":-0.22554135475887216},null,null,null,null,"stathera",{"$f":"IF(EPILOGI=1,STATHELXI,IF(EPILOGI=2,STATHAPOSI,STATHEL))","v":67017.841656797886},null,{"$f":"SQRT((S_3X-RTT_X)^2+(S_3Y-RTT_Y)^2)","v":11.687229325276443},{"$f":"VELOCITY3*BZ12","v":192.95630140986896},null,null,"rc",null,null,null,null,null,null,null,null,null,2.5,22.5,11.456439237389599,-6375,5815,48.228622207149975,0.54493719491262971,41.243181254602561,25,90,2.5,22.5,11.456439237389599,1929.1774745535256,1794.0359508241347,26.78832544840483,0.54493719491262971,22.908300329011865,13.886113796359609,192.95630140987004,2.5,22.5,11.456439237389599,18.051077305030365,34.837651927370189,3.7329694307545669,0.54493719491262971,3.1922855724391059,1.9350383962457194,-12.95630140986998,null,null,null,{"$f":"IF(EPILOGI=3,$DV$12&$DV$13&$DV$14&$DV$15,\"X\")","v":"X"},"Triangle SP'T similar to TDP\"   so ST/TD=SP'/DP\" =SP'/(K/V1)=SP'·V1/K"]
[{"$f":"A12+PI()/100","v":-1.4451326206513047},1.1279991020787403,-4.9605735065723886,71.808567800035149,-39.579075441529056,-71.242335794752307,39.89364877779731,null,-2.9845130209103039,-9.8768834059513786,-1.5643446504023053,7,"MHNYMA7","IP=HP      and     EP=   ES-SP    =    1/2·IS-SP=1/2(IP+SP)-SP   =   1/2(HP-SP)  =  a",null,null,null,null,null,null,1,2,-10.5,-14,null,"B",null,null,null,"L","QR/PV",{"$f":"SQRT((qx-rx)^2+(qy-ry)^2)/SQRT((PX-VX)^2+(PY-VY)^2)","v":{"$error":"#NUM!"}},"PX/PV",{"$f":"SQRT((PX-XX)^2+(PY-XY)^2)/SQRT((PX-VX)^2+(PY-VY)^2)","v":{"$error":"#NUM!"}},"y^2/b^2-x^2/a^2=1",null,"x^2*(tanpxi^2/b^2-1/a^2)=1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Fi3",35,"DDD_2",30,"FI3",0.66,-28,"kin energy"," ","TAN","perp","perp1",null,null,null,null,null,"energia",{"$f":"IF(EPILOGI=1,ENERGELXI,IF(EPILOGI=2,ENERGIAPS,ENERELAST))","v":3723.2134253776603},null,{"$f":"SQRT((S_3X-PTTX)^2+(S_3Y-PTTY)^2)","v":15.401756429090707},{"$f":"VELOCITY1*BZ13","v":323.29369740391076},null,null,{"$f":"BQ14","v":11.392517092150694},{"$f":"BR14","v":3.8805245642183177},null,null,null,null,null,null,null,null,3,27,14.142135623730951,-9290,8730,59.093146810776631,0.53248178357075504,50.911688245431428,30.000000000000004,90,3,27,14.142135623730951,1680.197201289446,2043.0162240882144,28.586823706653487,0.53248178357075504,24.628971970990609,14.512760911950725,192.95630140987004,3,27,14.142135623730951,13.805448712126429,30.592023334466255,3.4981151115688718,0.53248178357075504,3.0138003409618448,1.775898881863708,-12.95630140986998,null,-15,-7,-5,"Triangle STT similar to TT\"D\"   so ST/TD=ST'/DT\" =ST'/(K/V2)=ST'·V2/K"]
[{"$f":"A13+PI()/100","v":-1.4137166941154067},1.4079101853620803,-4.9384417029756884,57.532078993496853,-31.568757573375159,-56.823763632075284,31.962266107498252,null,-2.9321531433504742,-9.7814760073380569,-2.0791169081775887,8,"MHNYMA8","Draw QT perpendicular to SP; and putting L for the principal latus rectum of the hyperbola (that is, for 2BC²/AC), ",null,null,null,null,null,null,8,9,-16,-15,null,{"$f":"0","v":0},{"$f":"BBB","v":5},"L","2*BC^2/AC",{"$f":"2*BBB^2/AAA","v":5.5555555555555554},"PX/PV",{"$f":"SQRT((PX-XX)^2+(PY-XY)^2)/SQRT((PX-VX)^2+(PY-VY)^2)","v":{"$error":"#NUM!"}},"SINCE QR=PX",null,"y=tancpsi*x",null,"xk",{"$f":"1/SQRT(TAN(psi)^2/BBB^2-1/AAA^2)","v":3.0122433986692156},{"$f":"AL14*TAN(psi)","v":5.2726176614617843},null,null,"LINE","SPI",null,"DAA",0.4,null,null,null,null,null,null,null,null,null,null,null,null,null,"kk",45,"X1Y1",{"$f":"AAA/COS(BK13)","v":11.392517092150694},{"$f":"BBB*TAN(BK13)","v":3.8805245642183177},{"$f":"KIN3_","v":681.45127593651023},{"$f":"SQRT(2*BM14/MASS)/SMIK","v":5.5033374760190759},{"$f":"taNFR","v":0.90611692333589233},{"$f":"ATAN(BO16)","v":-0.83461196994636777},{"$f":"IF(vimata>0,BK14,BK14+1000)","v":11.392517092150694},{"$f":"IF(vimata>0,BL14,BL14+1000)","v":3.8805245642183177},{"$f":"BQ15-BQ14","v":-1.8301583731009785},{"$f":"BN14*COS(BO15)","v":4.0781712934208496},{"$f":"BN14*SIN(BO15)","v":3.6953000252312567},{"$f":"EPILOGI","v":2},null,null,null,{"$f":"SQRT((S_3X-TTT_X)^2+(S_3Y-TTT_Y)^2)","v":17.999919188787214},{"$f":"VELOCITY2*BZ14","v":192.95630140986881},null,null,{"$f":"BQ15","v":9.5623587190497155},{"$f":"BR15","v":5.9003062568096052},null,null,null,null,null,null,null,null,3.5,31.5,16.770509831248425,-12735,12175,69.785385289471606,0.52537524356361298,60.373835392494321,34.999999999999993,89.999999999999659,3.5,31.5,16.770509831248425,1488.1376689926058,2235.0757563850548,29.900339505664846,0.52537524356361298,25.867854250667172,14.996146805771877,192.95630140986981,3.5,31.5,16.770509831248425,11.176683366322454,27.963257988662281,3.3444436301819938,0.52537524356361298,2.8933979280980866,1.6773644878626144,-12.956301409869987,null,-15,-8,null,"TRIANGLE ST'V similar to VEV' so SV/VE=ST'/VE=ST'·V2/K"]
[-1.3823007675795087,1.6864318312715243,-4.9114362536434433,48.030402710632053,-26.210917905565836,-47.179652230018505,26.683557061462249,null,-2.8797932657906444,-9.6592582628906847,-2.5881904510252012,9,"MHNYMA9","L · QR/(L · Pv)    =  QR / Pv= Px/ Pv, that is (because of the similar triangles PXZ, PEC), PE /PC =a/PC=AC/ PC",null,null,null,null,null,null,-11,-3,-12,-14,null,0,0,null,"QR/QT²",{"$f":"SQRT((qx-rx)^2+(qy-ry)^2)/((qx-tx)^2+(qy-ry)^2)","v":{"$error":"#NUM!"}},"L/",null,"PE=AC","AC²/BC²",{"$f":"AAA^2/BBB^2","v":3.24},null,"xd",{"$f":"-AL14","v":-3.0122433986692156},{"$f":"AL15*TAN(psi)","v":-5.2726176614617843},null,"SPI",{"$f":"CCC","v":10.295630140987001},0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"mm",30,"X2Y2",{"$f":"BK14+SIGN(BL14)*BN14*COS(BO15)","v":15.470688385571544},{"$f":"BL14+(BO14)*(BK15-BK14)","v":7.5758245894495744},"SIGNX",{"$f":"SIGN(BK15-BK14)","v":1},{"$f":"ATAN(BO14)","v":0.73618435684852879},{"$f":"ATAN(BO14)","v":0.73618435684852879},{"$f":"IF(vimata>0,$CB$22,BQ14)","v":9.5623587190497155},{"$f":"IF(vimata>0,BR14+TAN(BP14)*(BQ15-BQ14),BR14)","v":5.9003062568096052},{"$f":"(BQ15-BQ14)*(BK15-BK14)+(BR15-BR14)*(BL15-BL14)","v":0},{"$f":"1/BN14*1*COS(BP14)*ddd_2","v":3.6603167462019561},{"$f":"1/BN14*1*SIN(BP14)*ddd_2","v":-4.0395633851825732},"potential",{"$f":"IF(EPILOGI=1,-stathe/SQRT((xp-CCC)^2+(yp_)^2),IF(EPILOGI=2,stathe/SQRT((xp+CCC)^2+(yp_)^2),-stathe*(xp^2+yp_^2)/2))","v":2621.6893771026639},{"$f":"IF(EPILOGI=1,-stathe/SQRT((XQ-CCC)^2+(YQ)^2),IF(EPILOGI=2,stathe/SQRT((XQ+CCC)^2+(YQ)^2),-stathe*(XQ^2+YQ^2)/2))","v":3435.9258592955521},{"$f":"IF(EPILOGI=1,-stathe/SQRT((XR-CCC)^2+(YR)^2),IF(EPILOGI=2,stathe/SQRT((XR+CCC)^2+(YR)^2),-stathe*(XR^2+YR^2)/2))","v":3041.7621494411501},null,"XP",{"$f":"AAA/COS(fi_1)","v":14.478532294194448},"YP_",{"$f":"BBB*TAN(fi_1)","v":-6.3007910877516959},"YP",null,"STATHERA","STATH2","STATH2","mass","mass",null,null,4,36,19.364916731037084,-16710,16150,80.37412518964048,0.52091340610427139,69.713700231733498,40.000000000000007,90.000000000000455,4,36,19.364916731037084,1335.4817754001913,2387.7316499774688,30.904573447808456,0.52091340610427139,26.805544247563418,15.380359475087282,192.95630140987009,4,36,19.364916731037084,9.3888961432252653,26.175470765565095,3.2357670352214849,0.52091340610427139,2.8065909592286373,1.6103525992161205,-12.956301409869972,null,null,null,{"$f":"IF(EPILOGI=3,$DV$16&$DV$17,\"X\")","v":"X"},"Triangle SRV similar to VER\"  SV/VE=SR'/ER=SR'·V3/K"]
[-1.3508848410436107,1.9632891725688861,-4.8795838096937363,41.257294713246296,-22.368714146057734,-40.263685462903922,22.920719285136833,null,-2.8274333882308147,-9.5105651629515382,-3.0901699437494665,10,"MHNYMA10","CV²/CP²-QV²/CD²=1  and since CV=CP+PV   (CP²+PV²+2CP·PV)/CP²-QV²/CD²=1",null,null,null,null,null,null,-17,-3,16,13,null,null,"X²/A²-Y²/B²=-1",null,"QX²/QT²=",{"$f":"((qx-XX)^2+(qy-XY)^2)/((qx-tx)^2+(qy-ty)^2)","v":{"$error":"#NUM!"}},null,"BA",null,null,"PC²/CD²",null,"DK",null,null,null,null,{"$f":"AP10","v":0.88361084154276071},{"$f":"AQ10","v":19.568094488069828},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X3Y3",{"$f":"BK15+BQ17","v":15.388755047510072},{"$f":"BL15+BR17","v":7.1843058439033305},"SIGNY",{"$f":"SIGN(BL15-BL14)","v":1},{"$f":"taNprpR","v":-1.1036103335521807},{"$f":"TAN(BP14)","v":-1.1036103335521807},"x","y",null,{"$f":"BT15*BT14","v":14.927398679188427},{"$f":"BU15*BU14","v":-14.927398679188423},"kinetic",{"$f":"energia-BW15","v":1101.5240482749964},{"$f":"energia-BX15","v":287.28756608210824},{"$f":"energia-BY15","v":681.45127593651023},null,"XQ",{"$f":"AAA/COS(fi_2)","v":9.1830496044707335},null,{"$f":"YQ","v":1.0135501775433626},"YQ",null,{"$f":"STATHERA","v":40.99684400566349},{"$f":"STATH2","v":7},{"$f":"STATH22","v":-363.71923023977314},{"$f":"MASS","v":5},{"$f":"mass_2","v":3},null,null,4.5,40.5,21.937410968480307,-21215,20655,90.895544445258707,0.51791973653417356,78.974679486529112,45,89.999999999999545,4.5,40.5,21.937410968480307,1211.2314318780539,2511.9819934996067,31.698466798882286,0.51791973653417356,27.541242763156077,15.693079508520491,192.95630140986987,4.5,40.5,21.937410968480307,8.0941769760929656,24.880751598432795,3.1547267138966437,0.51791973653417356,2.7409872796088903,1.5618224522638198,-12.956301409869987,null,-2,-8,null,"From the 4 equalities we get SP'·V1=ST'·V2=SR'·V3"]
[-1.3194689145077128,2.2382089844836965,-4.8429158056431545,36.189650100383652,-19.473714274649264,-35.052685694368677,20.105361166879806,null,-2.775073510670985,-9.3358042649720208,-3.5836794954529938,11,"MHNYMA11","1+PV²/CP²+2CP·PV/CP²-QV²/CD²=1  or since  2CP=GP  -PV²/CP²+GP·VP/CP²=QV²/CD²",null,null,null,null,null,null,null,null,null,null,null,null,"FOR X-0",null,"CA²/PF²",{"$f":"AAA^2/((PX-fx)^2+(PY-fy)^2)","v":1.4749642918713994},null,{"$f":"-AAA","v":-9},0,null,null,"cea",{"$f":"0","v":0},0,null,null,null,null,null,null,null,null,null,null,null,null,null,"charwidth",88.3,"yaxis",10,null,"gonia",null,null,null,null,"X4Y4",{"$f":"BK15+BQ18","v":15.073013137501222},{"$f":"BL15+BR18","v":7.5327618785246004},"F",{"$f":"-BO15","v":-0.73618435684852879},{"$f":"-BN15*DAA*COS(PI()/5)","v":-0.32360679774997902},{"$f":"-BN16*DAA*SIN(PI()/5)","v":-0.23511410091698925},{"$f":"BO17*COS(BN17)+BP17*SIN(BN17)","v":-8.1933338061471572E-2},{"$f":"-BO17*SIN(BN17)+BP17*COS(BN17)","v":-0.39151874554624411},null,null,null,"velocity",{"$f":"SQRT(2*BW16/MASS)","v":20.990703163781784},{"$f":"SQRT(2*BX16/MASS)","v":10.71984264963079},{"$f":"SQRT(2*BY16/MASS)","v":16.510012428057227},null,"XR",{"$f":"AAA/COS(fi_3)","v":11.392517092150694},null,{"$f":"BBB*TAN(fi_3)","v":3.8805245642183177},"YR",null,null,null,null,null,null,null,null,5,45,24.494897427831781,-26250,25690,101.3706071797935,0.51580999751098244,88.181630740194421,50.000000000000007,90.000000000000455,5,45,24.494897427831781,1108.1331170949518,2615.0803082827088,32.342419874107804,0.51580999751098244,28.134460332515385,15.952562963712188,192.95630140987021,5,45,24.494897427831781,7.1132650124294434,23.899839634769272,3.0919145935662109,0.51580999751098244,2.6896363606315861,1.5250547863851267,-12.956301409869965,null,-2,-9,null,"which means that the law of equal areas  is valid for the center C"]
[-1.2880529879718148,2.5109199543530671,-4.8014684283847151,32.259092871349409,-17.210112883346063,-30.978203190022917,17.921718261860782,null,-2.7227136331111552,-9.1354545764260138,-4.0673664307579918,12,"MHNYMA12","GV·VP/CP²=QV²/CD²   and     QT/QX=PF/PE=PF/AC       QT=  QX·PF/(PF·CD/BC)   =   QX·BC/CD = in the limit QV·BC/CD",null,null,null,null,null,null,-29,-29,12,-17,null,null,"Y=±B","B=BHYP","CONJ DIAM2",null,null,{"$f":"AAA","v":9},0,null,"TANSP",{"$f":"(PY-0)/(PX-CCC)","v":-2.0790537997754939},{"$f":"EX","v":5.5896204912648804},{"$f":"EY","v":9.784047244034916},null,null,null,null,null,null,null,null,null,null,null,null,null,"charheight",56,"xaxis",{"$f":"INT(yaxis*charwidth/charheight)","v":15},null,null,null,null,91,null,"X5Y5",{"$f":"BK15","v":15.470688385571544},{"$f":"BL15","v":7.5758245894495744},{"$f":"BK13","v":0.66},null,{"$f":"BO17","v":-0.32360679774997902},{"$f":"-BP17","v":0.23511410091698925},{"$f":"BO18*COS(BN17)+BP18*SIN(BN17)","v":-0.39767524807032201},{"$f":"-BO18*SIN(BN17)+BP18*COS(BN17)","v":-4.306271092497399E-2},null,null,"tanfp",{"$f":" (BBB / AAA) / SIN(fi_1)","v":-0.70922567414383086},"TanpRpp = -1 / tanFP",{"$f":"-1/tanfp","v":1.40998843732947},null,null,null,null,null,null,null,null,"LINE AD","ay","LINE CE",null,"LINE EBD",null,null,5.5,49.5,27.041634565979923,-31815,31255,111.81234278915723,0.51426563638629907,97.34988443752772,54.999999999999986,89.999999999998636,5.5,49.5,27.041634565979923,1021.2092251126994,2702.0042002649607,32.875548362057543,0.51426563638629907,28.623233840128524,16.171337750455461,192.95630140986964,5.5,49.5,27.041634565979923,6.3444034841601198,23.130978106499946,3.0417743576077401,0.51426563638629907,2.6483335811729711,1.4962354378344089,-12.956301409869994]
[-1.2566370614359168,2.7811529493745311,-4.7552825814757673,29.124611797498062,-15.388417685876242,-27.699151834577233,16.180339887498924,null,-2.6703537555513255,-8.9100652418836841,-4.5399049973954568,13,"MHNYMA13","L·QR/QT²=L·PV·AC/PC/(QV²·BC²/CD²)=L·PV·CD²·AC/PC/(QV²·BC²)",null,null,null,null,null,null,-29,-29,5,-12,null,null,null,"X2",{"$f":"BHYP*COS(psi)","v":3.0122433986692148},{"$f":"-BHYP*COS(psi)","v":-3.0122433986692148},null,"C",null,null,"point E","CUT OF SP WITH DK",null,"E",null,"perpendicular PF",null,"Y=PY-1/TAN(PSI)*(FX-PX)",null,null,null,null,null,null,null,null,null,"elastic force",null,"MQ",{"$f":"ry-TANTHETA*rx","v":0},null,null,null,"gonia",{"$f":"BH18-90","v":1},{"$f":"RADIANS(BH19)","v":1.7453292519943295E-2},null,null,null,null,null,null,null,null,null,null,null,"taNFq",{"$f":" (BBB / AAA) / SIN(fi_2)","v":2.7963830820401911},"taNprpQ",{"$f":" -1 / taNFq","v":-0.35760479543111018},null,null,null,{"$f":"ATAN(taNprpR)","v":-0.83461196994636777},null,{"$f":"kk","v":45},null,null,{"$f":"IF(vimata>1,$CB$20,$CB$20+1000)","v":13.238336276753014},{"$f":"IF(vimata>1,$CD$20,$CD$20+1000)","v":-8.0494531323661764},{"$f":"IF(vimata>1,CX,CX+1000)","v":9.5623587190497155},{"$f":"IF(vimata>1,XE,XE+1000)","v":4.9912223326776477},{"$f":"IF(vimata>1,BX,BX+1000)","v":5.2303625965643921},{"$f":"IF(vimata>1,XED,XED+1000)","v":3.8619718431880758},null,{"$f":"CN18+0.5","v":6},54,29.58039891549808,-37910,37350,122.22929272478018,0.51310033153283496,106.48943609579308,60.000000000000014,90.000000000001364,6,54,29.58039891549808,946.93035833000101,2776.2830670476592,33.324363862181428,0.51310033153283496,29.033079033887599,16.358286848906268,192.95630140987021,6,54,29.58039891549808,5.7255390528925503,22.512113675232378,3.0008074696809444,0.51310033153283496,2.6143839022115407,1.4730384522985507,-12.956301409869951]
[-1.2252211349000188,3.048641282207627,-4.7044038447711269,26.56921313528402,-13.888034269574852,-24.998461685234734,14.76067396404668,null,-2.6179938779914957,-8.6602540378443944,-4.9999999999999876,14,"MHNYMA14","L·PV·CD²·AC/PC/(QV²·BC²)=  L·PV·CD²·AC/PC/(GV·VP·CD²/CP²)=   2BC²·PC/(2PC·BC²)=1",null,null,null,null,null,null,-29,-29,-1,-6,null,null,null,"Y2",{"$f":"BHYP*SIN(psi)","v":5.2726176614617826},{"$f":"-BHYP*SIN(psi)","v":-5.2726176614617826},null,0,0,null,"Y=TANSP*(Ex-ccc)",null,"Ex",{"$f":"CCC*TANSP/(TANSP-TAN(psi))","v":5.5896204912648804},{"$f":"TANSP*(AL20-CCC)","v":9.784047244034916},{"$f":"PX","v":9.4907117906312095},{"$f":"PY","v":1.6734685548162302},"Y=TAN(PSI)*EX",null,null,null,null,null,null,null,null,null,"CR",{"$f":"rx","v":8.0907117906312092},{"$f":"ry","v":-0.7770853178580881},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PerPrxP2 = xp + Sgn(xp) * 1 / VELOCITY1 * kk * Cos(Atn(TanpRpp))",null,null,null,{"$f":" IF(vimata>0,xp + SIGN(xp) * 1 / VELOCITY1 * kk * COS(ATAN(TanpRpp)),xp)","v":15.718728311635882},{"$f":"IF(vimata>0,yp_ + TanpRpp * (AX - xp),yp_)","v":-8.0494531323661764},"AX",{"$f":"xp + PROS * SIGN(xp) * 1 / VELOCITY1 * kk * COS(ATAN(TanpRpp))","v":13.238336276753014},"AY",{"$f":"yp_+TanpRpp*(AX-xp)","v":-8.0494531323661764},null,null,{"$f":"IF(vimata>1,$CB$23,CG19)","v":3.8619718431880758},{"$f":"IF(vimata>1,$CD$23,CH19)","v":-1.3994947459528451},{"$f":"IF(vimata>1,CY,CY+1000)","v":5.9003062568096052},{"$f":"IF(vimata>1,YE,YE+1000)","v":1.758322218241398},{"$f":"IF(vimata>1,BY,BY+1000)","v":2.4270500064089169},{"$f":"IF(vimata>1,YD,YE+1000)","v":-1.3994947459528451},null,6.5,58.5,32.113081446662825,-44535,43975,132.62729734108285,0.51219894965397417,115.60709320798617,65,89.999999999999545,6.5,58.5,32.113081446662825,882.72435329968516,2840.4890720779749,33.707501076632632,0.51219894965397417,29.381781103123448,16.519884020153651,192.95630140986998,6.5,58.5,32.113081446662825,5.2166784844490932,22.003253106788922,2.966698711146039,0.51219894965397417,2.5859790653611787,1.4539647575609576,-12.956301409869965]
[-1.1938052083641209,3.3131209741621062,-4.6488824294412563,24.44824702499281,-12.628558447236504,-22.731405205025709,13.582359458329339,null,-2.565634000431666,-8.3867056794542485,-5.4463903501502573,15,"MHNYMA15",null,null,null,null,null,null,null,-29,-29,-8,-6,null,null,null,null,null,null,null,0,0,null,"y=tan(psi)*Ex",null,null,{"$f":"CCC","v":10.295630140987001},0,null,null,"FX*(1/TAN(PSI)+TAN(PSI))=PY+PX/TAN(PSI)",null,null,null,null,null,null,null,null,null,"TANTHETA",{"$f":"BB20/BA20","v":-9.6046594906263813E-2},null,"TANCD",{"$f":"DY/DX","v":1.7503956233387992},4,4,5,5,1,{"$f":"\"MHNYMA\"&TEXT(BI21,\"0\")","v":"MHNYMA1"},"F~QR/(PC²·QT²)",null,null,null,null,null,null,null,null,null,"SAB",{"$f":" BY - AY + AX * tanfp - BX * taNFq","v":-13.538562309616266},null,null,{"$f":"IF(vimata>0,XQ + SIGN(XQ) * 1 / VELOCITY2 * kk * COS(ATAN(taNprpQ)),XQ)","v":13.135736612377075},{"$f":"IF(vimata>0,YQ + taNprpQ * (BX - XQ),YQ)","v":2.4270500064089169},"BX",{"$f":" XQ + PROS * SIGN(XQ) * 1 / VELOCITY2 * kk * COS(ATAN(taNprpQ))","v":5.2303625965643921},"BY",{"$f":" YQ + taNprpQ * (BX - XQ)","v":2.4270500064089169},null,null,"D_3X","D_3Y","E_3X","E_3Y",null,null,null,7,63,34.641016151377542,-51690,51130,143.01048912579805,0.5114871244512994,124.70765814495915,70.000000000000014,90.000000000001819,7,63,34.641016151377542,826.67236434738436,2896.5410610302761,34.038455082628388,0.5114871244512994,29.682130633739838,16.660958719524913,192.95630140987055,7,63,34.641016151377542,4.7908857633827706,21.577460385722599,2.9378536645464561,0.5114871244512994,2.5618599916534652,1.4380047070348372,-12.956301409869937]
[-1.1623892818282229,3.5743310157130308,-4.5887731284199047,22.661583284793114,-11.554318269412034,-20.797772884941661,12.589768491551729,null,-2.5132741228718363,-8.0901699437494852,-5.8778525229247176,16,"MHNYMA16",null,null,null,null,null,null,null,null,null,null,null,null,null,"Tangent 1",null,null,null,"rectangula","1st tangent",null,"QT","QT","CUT OF Y=TANSP*(X-CCC)",null,null,null,null,null,"FX",{"$f":"(PY+PX/TAN(psi))/(TAN(psi)+1/TAN(psi))","v":3.0561751425679398},{"$f":"AQ22*TAN(psi)","v":5.3495155937077516},null,null,null,null,null,null,null,"FIND QQ","ALFAQQ",{"$f":"AAA^2*TANTHETA^2-BBB^2","v":-24.252779180159877},"TANQT",{"$f":"-1/TANPC","v":-5.6712818196177093},2,2,2,2,{"$f":"BI21+1","v":2},{"$f":"\"MHNYMA\"&TEXT(BI22,\"0\")","v":"MHNYMA2"},"GV·VP/CP²=QV²/CD²             QV²=GV·VP·CD² /CP²",null,null,null,null,null,null,null,null,null,"taNFR ",{"$f":" (BBB / AAA) / SIN(fi_3)","v":0.90611692333589233},"taNprpR ",{"$f":" -1 / taNFR","v":-1.1036103335521807},{"$f":"IF(vimata>0,XR + SIGN(XR) * 1 / VELOCITY3 * kk * COS(ATAN(taNprpR)),XR)","v":13.222675465251672},{"$f":" IF(vimata>0,YR + taNprpR * (CX - XR),YR)","v":5.9003062568096052},"CX",{"$f":" XR + PROS * SIGN(XR) * 1 / VELOCITY3 * kk * COS(ATAN(taNprpR))","v":9.5623587190497155},"CY",{"$f":"YR + taNprpR * (CX - XR)","v":5.9003062568096052},null,null,null,"LINE RZ","R_3Y","LINE PT",null,null,null,7.5,67.5,37.165171868296262,-59375,58815,153.38187637397058,0.51091503298168517,133.79461872586654,74.999999999999986,90,7.5,67.5,37.165171868296262,777.31382371520658,2945.8996016624537,34.327246330939239,0.51091503298168517,29.94356923603479,16.785186983521289,192.95630140986987,7.5,67.5,37.165171868296262,4.4293554673106046,21.215930089650431,2.9131378333096722,0.51091503298168517,2.5411226861852922,1.4244534143363961,-12.956301409869965]
[-1.1309733552923249,3.8320136240856595,-4.5241352623300966,21.137711904489137,-10.625540865785997,-19.125973558414792,11.743173280271742,null,-2.4609142453120065,-7.7714596145697197,-6.2932039104983604,17,"MHNYMA17",null,null,null,null,null,null,null,null,null,null,null,null,null,"x1",{"$f":"-Ahyp","v":-9.6371213179447413},{"$f":"BHYP","v":6.0724053962811952},"y1","x1",{"$f":"AB23*COS(phi)+AC23*COS(psi)","v":-6.4784683919619948},{"$f":"AB23*SIN(phi)+AC23*SIN(psi)","v":3.5991491066455525},{"$f":"(qy+qx/TANSP+CCC*TANSP)/(TANSP+1/TANSP)","v":{"$error":"#NUM!"}},{"$f":"TANSP*(AH23-CCC)","v":{"$error":"#NUM!"}},"TY","AND Y=QY-1/TANSP*(X-QX)",null,null,null,null,"PX",{"$f":"PX","v":9.4907117906312095},{"$f":"PY","v":1.6734685548162302},null,null,null,null,null,null,null,null,"BETAQQ",{"$f":"AAA^2*TANTHETA*MQ","v":0},"TANPC",{"$f":"PY/PX","v":0.17632698070846498},2,2,-2,-5,{"$f":"BI22+1","v":3},"MHNYMA3","FROM SIMILAR TRIANGLES QTV AND PCF  QV²/QT²=PC²/PF²   QT²=QV²· PF²/PC²=GV·VP·CD² /CP²  · PF²/PC²",null,null,null,null,null,null,null,null,null,"SCB ",{"$f":" BY - CY + CX * taNFR - BX * taNFq","v":-9.4347386660296877},null,null,{"$f":" SAB / (tanfp - taNFq)","v":3.8619718431880758},{"$f":" AY + tanfp * (XED - AX)","v":-1.3994947459528451},"XD(XED)",{"$f":"SAB/(tanfp-taNFq)","v":3.8619718431880758},"YD",{"$f":" AY + tanfp * (XED - AX)","v":-1.3994947459528451},null,null,"R_3X",{"$f":"CB30","v":11.392517092150694},{"$f":"CD30","v":3.8805245642183177},{"$f":"xp","v":14.478532294194448},{"$f":"yp_","v":-6.3007910877516959},"P_3Y",null,8,72,39.686269665968858,-67590,67030,163.74370216896892,0.51044825358556523,142.87057079748789,80,90,8,72,39.686269665968858,733.51733693179153,2989.6960884458686,34.581475321020463,0.51044825358556523,30.173222253367015,16.89541636738393,192.95630140987009,8,72,39.686269665968858,4.1185602646275603,20.905134886967389,2.8917216247050743,0.51044825358556523,2.5231011247243411,1.4128038325265544,-12.956301409869951]
[-1.0995574287564269,4.085914497655927,-4.4550326209418376,19.824203381267374,-9.8130525275257359,-17.663494549546325,11.013446322926319,null,-2.4085543677521768,-7.4314482547739562,-6.6913060635885682,18,"MHNYMA18",null,null,null,null,null,"QT/QX=PF/PE=PF/AC  QT=QX·PF/(PF·CD/BC)=QX·BC/CD",null,null,null,null,null,null,null,"x2",{"$f":"-Ahyp","v":-9.6371213179447413},{"$f":"0","v":0},"h2",null,{"$f":"AB24*COS(phi)+AC24*COS(psi)","v":-9.4907117906312095},null,{"$f":"qx","v":{"$error":"#NUM!"}},{"$f":"qy","v":{"$error":"#NUM!"}},null,"X*(TANSP+1/TANSP)=(QY+QX/TANSP+CCC*TANSP)",null,null,null,null,null,"PF",null,null,null,null,null,null,null,null,null,"GAMAQQ",{"$f":"AAA^2*(MQ^2+BBB^2)","v":2025},null,null,3,3,-4,-4,4,"MHNYMA4","COMBINING WE GET QR/(PC²·QT²)=QR/(PC²·GV·PV·CD²·PF²/PC^4)=  QR/(PC²·QT²)=QR/(PC²·2PC·PV·CD²·PF²/PC^4)=PC/(2CD²·PF²)  Q.E.D.",null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SCB/(taNFR-taNFq)","v":4.9912223326776477},{"$f":" BY + taNFq * (XE - BX)","v":1.758322218241398},"XE",{"$f":"SCB/(taNFR-taNFq)","v":4.9912223326776477},"YE",{"$f":"YB+taNFq*(XE-BX)","v":1.758322218241398},null,null,"v_3X",{"$f":"IF(vimata>2,CB26,r_3x)","v":9.640624586990965},{"$f":"IF(vimata>2,CD26,r_3y)","v":2.2931051174277743},{"$f":"IF(vimata>2,CB25,CJ23)","v":8.1679194994693738},{"$f":"IF(vimata>2,CD25,CK23)","v":-1.8251424741521207},"T_3Y",null,8.5,76.5,42.204857540335333,-76335,75775,174.09767373517661,0.51006237290142098,151.9374871452072,85.000000000000014,90,8.5,76.5,42.204857540335333,694.39289537797549,3028.8205299996848,34.807013833419752,0.51006237290142098,30.376570251723688,16.993886893291048,192.95630140987009,8.5,76.5,42.204857540335333,3.8485205841781269,20.635095206517953,2.8729841772288238,0.51006237290142098,2.5072936767672043,1.4026818958874374,-12.956301409869965]
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[-1.005309649148733,4.822441154810976,-4.2216396275100729,16.796472450305085,-7.8787392998432404,-14.181730739717832,9.3313735835028258,null,-2.2514747350726876,-6.2932039104983941,-7.771459614569693,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X1",{"$f":"-Ahyp","v":-9.6371213179447413},{"$f":"BHYP","v":6.0724053962811952},null,null,{"$f":"AB27*COS(phi)+AC27*COS(psi)","v":-6.4784683919619948},{"$f":"AB27*SIN(phi)+AC27*SIN(psi)","v":3.5991491066455525},null,"FOR Y =BHYP",null,"X=AHYP*SQRT(2)",null,null,null,null,null,null,null,"XX",{"$f":"(qy+CCC*TANSP-TAN(psi)*qx)/(TANSP-TAN(psi))","v":{"$error":"#NUM!"}},{"$f":"TANSP*(AT27-CCC)","v":{"$error":"#NUM!"}},"XY",null,null,null,null,"QQY",{"$f":"ry+TANTHETA*(QQX-rx)","v":-0.87763458693362439},{"$f":"ry","v":-0.7770853178580881},0,{"$f":"DEGREES(BF27)","v":-180},{"$f":"-PI()","v":-3.1415926535897931},{"$f":"IF(ABS(COS($BF27))>0.0000000001,AAA/COS($BF27),\"\")","v":-9},{"$f":"IF(ABS(COS($BF27))>0.0000000001,BBB*TAN($BF27),\"\")","v":6.1257422745431001E-16},7,"MHNYMA7",null,null,null,null,null,null,{"$f":"-PI()","v":-3.1415926535897931},{"$f":"x_ken+r_cakmp*COS($BQ27)","v":8.9999986719635618},{"$f":"y_ken+r_cakmp*SIN(BQ27)","v":-1.1274577254200794E-4},null,"TaNTd ",{"$f":" (YT - YD) / (XT - XED)","v":-9.8851115288956751E-2},"Stv ",{"$f":" YZ - YT + XT * TaNTd - XZ * TanVE","v":2.2019570596007698},{"$f":" Stv / (TaNTd - TanVE)","v":-10.295630140986898},{"$f":" YT + TaNTd * (S_3X - XT)","v":-1.7763568394002505E-15},"XS",{"$f":"Stv/(TaNTd-TanVE)","v":-10.295630140986898},"YS",{"$f":"YT + TaNTd * (S_3X - XT)","v":-1.7763568394002505E-15},null,null,{"$f":"(v_3y-r_3y)/(v_3x-r_3x)","v":0.90611692333589289},{"$f":"IF(vimata>2,CH24,CH24+1000)","v":9.640624586990965},{"$f":"IF(vimata>2,CI24,CI24+1000)","v":2.2931051174277743},"TAN1",{"$f":"(CI24-CJ20)/(CH24-CI20)","v":0.14297791042840086},null,null,10,90,49.749371855330999,-105750,105190,205.12435252792389,0.50923465819548752,179.09773867919159,99.999999999999986,89.999999999998181,10,90,49.749371855330999,598.60714236572335,3124.6062830119372,35.35311178955503,0.50923465819548752,30.867433821247701,17.234965694647276,192.95630140986964,10,90,49.749371855330999,3.2159454838904273,20.002520106230254,2.8286053175535293,0.50923465819548752,2.4697058625489627,1.3789709913494872,-12.956301409869994]
[-0.97389372261283502,5.0587504006691821,-4.1354028713728059,16.011859369318785,-7.3572765790998318,-13.243097842379697,8.8954774273993245,null,-2.1991148575128578,-5.8778525229247522,-8.0901699437494585,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X2",0,{"$f":"BHYP","v":6.0724053962811952},null,null,{"$f":"AB28*COS(phi)+AC28*COS(psi)","v":3.0122433986692148},{"$f":"AB28*SIN(phi)+AC28*SIN(psi)","v":5.2726176614617826},null,{"$f":"-Ahyp*SQRT(2)","v":-13.62894767007233},{"$f":"BHYP","v":6.0724053962811952},null,null,{"$f":"AI28*COS(phi)+AJ28*COS(psi)","v":-10.409649932215684},{"$f":"AI28*SIN(phi)+AJ28*SIN(psi)","v":2.9059757350357662},null,null,null,null,"QX",{"$f":"qx","v":{"$error":"#NUM!"}},{"$f":"qy","v":{"$error":"#NUM!"}},null,null,null,null,null,null,"TTX",{"$f":"(QQY-TANQT*QQX)/(TANPC-TANQT)","v":8.711975429373112},{"$f":"QQX","v":9.1375918926657143},{"$f":"DEGREES(BF28)","v":-176.4},{"$f":"BF27+PI()/50","v":-3.0787608005179972},-9.0177945576402792,0.31457333626824985,8,"MHNYMA8",null,null,null,null,null,null,{"$f":"BQ27+PI()/50","v":-3.0787608005179972},9.005490606779329,-0.17486894519478127,null,"TanVE ",{"$f":" (YZ - YE) / (XZ - XE)","v":0.11502186086184532},null,null,{"$f":"TaNTd","v":-9.8851115288956751E-2},null,"XP",{"$f":"xp","v":14.478532294194448},"YP",-12.168185134131933,null,null,null,{"$f":"IF(vimata>2,CJ24,CH27)","v":8.1679194994693738},{"$f":"IF(vimata>2,CK24,CI27)","v":-1.8251424741521207},null,"X1",{"$f":"CH24","v":9.640624586990965},{"$f":"IF(vimata>3,CB24,CL28)","v":4.9912223326776477},10.5,94.5,52.261362400917186,-116615,116055,215.45765245170568,0.50903491204914242,188.14090464330184,104.99999999999999,89.999999999998181,10.5,94.5,52.261362400917186,572.29279098857057,3150.9206343890896,35.501665506784832,0.50903491204914242,31.000595192540473,17.301195087735191,192.95630140986964,10.5,94.5,52.261362400917186,3.0488980067945906,19.835472629134419,2.8167692577940722,0.50903491204914242,2.4596458297140575,1.3727095264563489,-12.956301409870008]
[-0.94247779607693705,5.2900672706322656,-4.0450849718747346,15.311714550336699,-6.8819096023558544,-12.387437284240539,8.5065080835203872,null,-2.1467549799530281,-5.4463903501502937,-8.3867056794542254,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X3=",{"$f":"Ahyp","v":9.6371213179447413},{"$f":"BHYP","v":6.0724053962811952},null,null,{"$f":"AB29*COS(phi)+AC29*COS(psi)","v":12.502955189300424},{"$f":"AB29*SIN(phi)+AC29*SIN(psi)","v":6.9460862162780126},null,{"$f":"-AI28","v":13.62894767007233},{"$f":"BHYP","v":6.0724053962811952},null,null,{"$f":"AI29*COS(phi)+AJ29*COS(psi)","v":16.434136729554112},{"$f":"AI29*SIN(phi)+AJ29*SIN(psi)","v":7.6392595878877989},null,null,null,null,null,null,null,"FIND V AS CUT  OF gp and qx",null,null,null,null,null,"TTY",{"$f":"TANPC*TTX","v":1.5361563234676936},{"$f":"QQY","v":-0.87763458693362439},-172.79999999999998,{"$f":"BF28+PI()/50","v":-3.0159289474462012},-9.0715317372836761,0.63164689223054238,9,"MHNYMA9",null,null,null,null,null,null,{"$f":"BQ28+PI()/50","v":-3.0159289474462012},9.0219447370689423,-0.3489354617364141,null,null,null,null,null,null,null,"XQ",{"$f":"AAA/COS(fi_2)","v":9.1830496044707335},"YQ",{"$f":"BBB*TAN(fi_2)","v":1.0135501775433626},null,null,null,null,null,null,"Y1",{"$f":"IF(vimata>2,CI24,CL28)","v":2.2931051174277743},{"$f":"IF(vimata>2,CD24,CM28)","v":1.758322218241398},11,99,54.772255750516614,-128010,127450,225.78751072634643,0.50886197124952703,197.18012070185981,110.00000000000001,90.000000000001819,11,99,54.772255750516614,548.19454225897744,3175.0188831186829,35.637165336870908,0.50886197124952703,31.121918745598663,17.361846872951851,192.95630140987009,11,99,54.772255750516614,2.8983476728651105,19.684922295204938,2.8060593219107068,0.50886197124952703,2.4505302087391736,1.36706642638122,-12.95630140986998]
[-0.91106186954103907,5.5161634828767951,-3.9507750618784487,14.684118817623729,-6.4459611589253205,-11.602730086065577,8.1578437875687388,null,-2.0943951023931984,-5.0000000000000249,-8.6602540378443713,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"TANGENT3",null,null,null,"pr",1.4,null,null,"find Q","y=ry+tspI(qx-rx)",null,null,"bbb^2*(qx^2/AAA^2-1)=ry^2+tsp^2*(qx^2-2*qx*rx+rx^2)+2*ry*tsp*(qx-rx)",null,null,null,null,null,null,null,null,"y=tan(phi)*x",null,"x*(tan(phi)-tan(psi))=(qy-tan(psi)*qx)",null,null,null,"VQ",null,null,-169.2,-2.9530970943744053,-9.1622893337193823,0.95380101109283577,10,"MHNYMA10",null,null,null,null,null,null,-2.9530970943744053,9.0492961258973246,-0.52162533438007785,null,null,null,null,null,{"$f":"CCC","v":10.295630140987001},null,"XR",{"$f":"AAA/COS(fi_3)","v":11.392517092150694},"YR",{"$f":"BBB*TAN(fi_3)","v":3.8805245642183177},null,null,null,null,null,null,"LINE DT",null,null,11.5,103.5,57.282196186947999,-139935,139375,236.1143790623519,0.50871123862085688,206.21590627301279,115.00000000000001,90.000000000001819,11.5,103.5,57.282196186947999,526.04375938033922,3197.1696659973213,35.761262091807225,0.50871123862085688,31.232918134906694,17.417597170021615,192.95630140987055,11.5,103.5,57.282196186947999,2.7619656583660666,19.548540280705893,2.796321889962305,0.50871123862085688,2.4422318329768595,1.36195439948511,-12.956301409869937]
[-0.8796459430051411,5.7368159077382144,-3.8525662138789429,14.119330531548274,-6.043961752048034,-10.87913115368646,7.8440725175268184,null,-2.0420352248333686,-4.539904997395495,-8.9100652418836646,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X1",{"$f":"Ahyp","v":9.6371213179447413},{"$f":"BHYP","v":6.0724053962811952},null,"zx",{"$f":"PX+pr","v":10.89071179063121},{"$f":"PY+TAN(psi)*pr","v":4.1240224274905488},"zy",null,"y-bbb*sqrt(s^2/AAA^2-1)",null,null,"qx^2*((bbb/AAAz)^2-tsp^2)+2*(tsp^2*rx*-ry*tsp)*qx-bbb^2-ry^2+2*ry*tsp*rx-rx^2*tsp^2",null,null,null,null,null,null,null,null,"y=qy+tan(psi)*(x-qx)",null,"vx",{"$f":"(qy-TAN(psi)*qx)/(TAN(phi)-TAN(psi))","v":{"$error":"#NUM!"}},{"$f":"TAN(phi)*(AY31)","v":{"$error":"#NUM!"}},"vy","VXX",{"$f":"(QQY-QQX*TANCD)/(TANPC-TANCD)","v":10.718741855830322},{"$f":"QQX","v":9.1375918926657143},-165.59999999999997,-2.8902652413026093,-9.2919228427560601,1.2837818018386367,11,"MHNYMA11",null,null,null,null,null,null,-2.8902652413026093,9.087436829828432,-0.69225703509294578,null,null,"PIGIOX",{"$f":"IF(EPILOGI=1,CCC,IF(EPILOGI=2,-CCC,0))","v":-10.295630140987001},null,null,null,"VELOCITY1",{"$f":"SQRT(2*KIN1_/MASS)","v":20.990703163781784},null,"FI1",-1.0995574287564276,null,null,null,null,"TAN2",{"$f":"(CK24-CH20)/(CJ24-CG20)","v":-9.8851115288956751E-2},null,null,12,108,59.791303715506992,-152390,151830,246.4386333349542,0.50857906318111912,215.24869337582516,120.00000000000001,90.000000000001819,12,108,59.791303715506992,505.61353827545861,3217.5998871022016,35.875339090256425,0.50857906318111912,31.334859145630048,17.469017063487161,192.95630140987009,12,108,59.791303715506992,2.6378417727911661,19.424416395130994,2.7874300992226511,0.50857906318111912,2.4346454069099939,1.3573018458192965,-12.956301409869951]
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[-0.78539816339744717,6.3639610306789347,-3.5355339059327333,12.727922061357841,-4.9999999999999885,-8.9999999999999787,7.0710678118654666,null,-1.8849555921538788,-3.0901699437495012,-9.5105651629515275,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"TANGENT4",null,null,null,null,null,null,null,null,null,null,null,"gamaq",{"$f":"AAA^2*(M^2+BBB^2)","v":22875.048279500959},"qy",{"$f":"ry+TANSP*(AP33-rx)","v":{"$error":"#NUM!"}},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"VYY","v":1.8900033884320093},{"$f":"PY","v":1.6734685548162302},-154.79999999999995,-2.7017696820872215,-9.946652208807599,2.3528214060612616,14,"MHNYMA14",null,"aktina kampylothtaw",null,null,null,null,-2.7017696820872215,9.2648804204110498,-1.1851255684785058,null,null,null,null,null,null,null,null,"AAA",7,"KIN1",{"$f":"KIN1_","v":1101.5240482749964},null,null,null,{"$f":"CI33","v":-10.295630140986898},{"$f":"CJ33","v":-1.7763568394002505E-15}]
[-0.75398223686154919,6.5607176467927113,-3.4227355296434392,12.346210332584251,-4.6953125290874507,-8.4515625523574123,6.8590057403245837,null,-1.8325957145940488,-2.588190451025234,-9.6592582628906758,null,null,null,null,null,null,null,null,"                                                                                                                                                                           ",null,null,null,null,null,null,"X1",{"$f":"Ahyp","v":9.6371213179447413},{"$f":"-BHYP","v":-6.0724053962811952},null,null,{"$f":"AB35*COS(phi)+AC35*COS(psi)","v":6.4784683919619948},{"$f":"AB35*SIN(phi)+AC35*SIN(psi)","v":-3.5991491066455525},null,{"$f":"-Ahyp*SQRT(2)","v":-13.62894767007233},{"$f":"-BHYP","v":-6.0724053962811952},null,null,{"$f":"AI35*COS(phi)+AJ35*COS(psi)","v":-16.434136729554112},{"$f":"AI35*SIN(phi)+AJ35*SIN(psi)","v":-7.6392595878877989},null,{"$f":"qx","v":{"$error":"#NUM!"}},{"$f":"qy","v":{"$error":"#NUM!"}},{"$f":"XX","v":{"$error":"#NUM!"}},{"$f":"tx","v":{"$error":"#NUM!"}},null,null,null,null,null,null,null,null,null,null,null,-151.19999999999996,-2.6389378290154255,-10.270377032330174,2.7487732609638553,15,"MHNYMA15","r_cakmp",{"$f":"1/(AAA*BBB)*(AAA^2*SIN(gonia)^2+BBB^2)^(3/2)/COS(gonia)^3","v":2.7831621832760143},null,{"$f":"aktin","v":2.7777777777777777},"=BBB^2/AAA",null,-2.6389378290154255,9.3442572423893413,-1.3409113531867149,null,null,null,null,null,null,null,null,"BBB",6.2,"KIN2",{"$f":"KIN2_","v":287.28756608210824},null,null,null,{"$f":"CCC","v":10.295630140987001},null,null,"SSAA","RTT_X","RTT_Y",null,null,"DT'\""]
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[-0.69115038378975324,6.9346191849821102,-3.1871199487434438,11.680526044662532,-4.1363597298623676,-7.4454475137522609,6.4891811359236291,null,-1.7278759594743889,-1.5643446504023342,-9.8768834059513733,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X3=",{"$f":"-Ahyp","v":-9.6371213179447413},{"$f":"-BHYP","v":-6.0724053962811952},null,null,{"$f":"AB37*COS(phi)+AC37*COS(psi)","v":-12.502955189300424},{"$f":"AB37*SIN(phi)+AC37*SIN(psi)","v":-6.9460862162780126},null,null,null,null,null,null,null,null,"QR",null,"TX",null,null,null,null,null,null,null,null,null,null,null,null,-143.99999999999994,-2.5132741228718336,-11.124611797498115,3.6327126400268117,17,"MHNYMA17","y_ken",{"$f":"yshmeio+r_cakmp*SIN(ATAN(tankath))","v":-1.1274577254166696E-4},{"$f":"yshmeio","v":8.727532464108792E-2},null,null,null,-2.5132741228718336,9.5315353508675997,-1.6360144318403063,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"KATH FROM S",{"$f":"-1/CK36","v":-1.1036103335521801},"LINE SR'",{"$f":"IF(vimata>3,S_3X,PIGIOX+1000)","v":-10.295630140986898},{"$f":"IF(vimata>3,S_3Y,1000)","v":-1.7763568394002505E-15},null,null,"rtt_y",{"$f":"r_3y+CK36*(CR36-r_3x)","v":-8.6606578901728799}]
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[-0.62831853071795729,7.2811529493745342,-2.9389262614623601,11.124611797498096,-3.6327126400267939,-6.5388827520482291,6.1803398874989419,null,-1.623156204354729,-0.5233595624294628,-9.9862953475457381,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"-Ahyp*SQRT(2)","v":-13.62894767007233},{"$f":"BHYP","v":6.0724053962811952},null,null,{"$f":"AI39*COS(phi)+AJ39*COS(psi)","v":-10.409649932215684},{"$f":"AI39*SIN(phi)+AJ39*SIN(psi)","v":2.9059757350357662},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-136.79999999999993,-2.3876104167282417,-12.346210332584278,4.6953125290874729,"=1/(AAA*BBB)*(AAA^2*SIN(gonia)^2+BBB^2)^(3/2)/COS(gonia)^3/2",null,null,null,null,null,null,null,-2.3876104167282417,9.7543229386056822,-1.9053183636643101,null,null,null,null,null,null,null,null,{"$f":"VAPELXI","v":2.3321342537766014},null,null,null,"x",{"$f":"IF(vimata>3,S_3X,PIGIOX)","v":-10.295630140986898},{"$f":"IF(vimata>3,CB25,PIGIOX)","v":8.1679194994693738},{"$f":"IF(vimata>3,CB27,XZ)","v":-10.295630140986898},{"$f":"CB26","v":9.640624586990965},null,null,{"$f":"IF(vimata>2,r_3x,r_3x+1000)","v":11.392517092150694},{"$f":"IF(vimata>3,r_3y,r_3y+1000)","v":3.8805245642183177}]
[-0.59690260418205932,7.4437251684710635,-2.8104168892606474,10.88164839065886,-3.3979964911226226,-6.1163936840207205,6.0453602170326999,null,-1.570796326794899,-2.3812332314299134E-14,-10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AI39","v":-13.62894767007233},{"$f":"-BHYP","v":-6.0724053962811952},null,null,{"$f":"AI40*COS(phi)+AJ40*COS(psi)","v":-16.434136729554112},{"$f":"AI40*SIN(phi)+AJ40*SIN(psi)","v":-7.6392595878877989},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-133.19999999999993,-2.3247785636564458,-13.147378642102636,5.3244592016239718,null,null,null,null,null,null,null,null,-2.3247785636564458,9.8779552373478126,-2.0289506624064391,null,null,null,null,null,null,null,null,null,null,null,null,"y",{"$f":"IF(vimata>3,CD27,0)","v":-1.7763568394002505E-15},{"$f":"IF(vimata>3,CD25,0)","v":-1.8251424741521207},{"$f":"IF(vimata>3,CD27,YZ)","v":-1.7763568394002505E-15},{"$f":"CD26","v":2.2931051174277743},null,"LINE SP'",{"$f":"IF(vimata>3,S_3X,S_3X+1000)","v":-10.295630140986898},{"$f":"IF(vimata>3,S_3Y,S_3Y+1000)","v":-1.7763568394002505E-15}]
[-0.56548667764616134,7.598951329518143,-2.6791339748949774,10.659365547632254,-3.1730964877207302,-5.7115736778973147,5.9218697486845855,null,-1.518436449235069,0.52335956242941528,-9.9862953475457399,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"REPULSIVE FORCE",null,null,null,null,null,null,"line // to TANGENT 3",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-129.59999999999994,-2.2619467105846498,-14.119330531548316,6.0439617520480615,null,null,null,null,null,null,null,null,-2.2619467105846498,10.009106512258107,-2.1445760647794909,null,null,null,null,null,"line RR\"",{"$f":"IF(vimata>2,r_3x,rx+1000)","v":11.392517092150694},{"$f":"IF(vimata>2,r_3y,ry+1000)","v":3.8805245642183177},null,null,null,null,null,null,null,null,"TANTP",{"$f":"(t_3y-yp_)/(t_3x-xp)","v":-0.70922567414383086},{"$f":"S_3Y-yp_++xp*tanfp-S_3X*(-1/tanfp)","v":10.548963714600717},{"$f":"IF(vimata>3,CL41/(tanfp+1/tanfp),PIGIOX+1000)","v":-4.9777715510147118},{"$f":"IF(vimata>3,yp_+tanfp*(CM41-xp),1000)","v":7.4981191232139786},null,"ptx",{"$f":"CL41/(tanfp+1/tanfp)","v":-4.9777715510147118}]
[-0.53407075111026336,7.7466782430354995,-2.5452070787518499,10.456094529654884,-2.9569917569973452,-5.3225851625952219,5.8089414053638242,null,-1.4660765716752391,1.0452846326765126,-9.9452189536827369,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"-CCC","v":-10.295630140987001},0,null,null,null,null,null,null,{"$f":"Ahyp*SQRT(2)","v":13.62894767007233},{"$f":"BHYP","v":6.0724053962811952},null,null,{"$f":"AI42*COS(phi)+AJ42*COS(psi)","v":16.434136729554112},{"$f":"AI42*SIN(phi)+AJ42*SIN(psi)","v":7.6392595878877989},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-125.99999999999993,-2.1991148575128538,-15.311714550336747,6.8819096023558881,null,null,null,null,null,null,null,null,-2.1991148575128538,10.147259169171816,-2.2517382501445216,null,null,null,null,null,null,{"$f":"IF(vimata>2,RTTX,RTTX+1000)","v":7.3205899438976818},{"$f":"IF(vimata>2,RTTY,RTTY+1000)","v":0.19088246459540414},null,null,null,null,null,null,null,null,"KATH FROM S",{"$f":"-1/CK41","v":1.40998843732947},null,{"$f":"PTTX","v":5.1021678606295113},{"$f":"PTTY","v":0.34916729866163543},null,"pty",{"$f":"yp_+tanfp*(PTX-xp)","v":7.4981191232139786}]
[-0.50265482457436539,7.8867601203947792,-2.4087683705085698,{"$f":"IF(ABS(COS(A43))>0.0000000001,AAA/COS(A43),D42)","v":10.270377032330162},{"$f":"IF(ABS(COS(A43))>0.0000000001,BBB*TAN(A43),E42)","v":-2.7487732609638407},{"$f":"IF(ABS(COS(A43))>0.001,AAA*TAN(A43),F42)","v":-4.947791869734913},{"$f":"IF(ABS(COS($A43))>0.0001,BBB/COS(A43),G42)","v":5.7057650179612009},null,-1.4137166941154091,1.5643446504022873,-9.8768834059513804,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"PX","v":9.4907117906312095},{"$f":"PY","v":1.6734685548162302},null,null,null,"T_1X","t_1Y",null,{"$f":"AI42","v":13.62894767007233},{"$f":"-BHYP","v":-6.0724053962811952},null,null,{"$f":"AI43*COS(phi)+AJ43*COS(psi)","v":10.409649932215684},{"$f":"AI43*SIN(phi)+AJ43*SIN(psi)","v":-2.9059757350357662},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-122.39999999999992,-2.1362830044410579,-16.796472450305149,7.8787392998432813,null,null,null,null,null,null,null,null,-2.1362830044410579,10.291867982668046,-2.3500142983136398,null,null,null,null,null,null,null,null,null,null,null,null,null,"ST'"]
[-0.47123889803846747,8.0190587176953176,-2.2699524986977271,10.100936138709239,-2.5476272474721346,-4.5857290454498418,5.6116311881718,null,-1.3613568165555792,2.0791169081775731,-9.7814760073380604,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"QT2",null,"TANHP",{"$f":"(PY-0)/(PX+CCC)","v":8.4576955184528485E-2},{"$f":"qq_y+(-CCC)*AD44-qq_x*AD45","v":105.8652341993018},{"$f":"AE44/(TANHP-AD45)","v":8.8901654912852841},{"$f":"AD44*(AF44+CCC)","v":1.6226761773702154},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-118.79999999999991,-2.0734511513692619,-18.68174646883919,9.0949662364053658,null,null,null,null,null,null,null,null,-2.0734511513692619,10.442362247825407,-2.4390163586227787,null,null,"SCB  ",{"$f":" YB - CY + CX * taNFR - BX * taNFq","v":-9.4347386660296877},null,null,null,null,null,null,null,null,"x",{"$f":"IF(vimata>3,S_3X,XR)","v":-10.295630140986898},{"$f":"CB30","v":11.392517092150694},{"$f":"CB32","v":10.71984264963079},{"$f":"CB31","v":20.990703163781784},null,"ST'",{"$f":"IF(vimata>3,r_3x,XR)","v":11.392517092150694},{"$f":"IF(vimata>3,r_3y,ry)","v":3.8805245642183177}]
[-0.43982297150256955,8.143443472194182,-2.1288964578253564,9.9466522088075902,-2.3528214060612482,-4.235078530910247,5.5259178937819939,null,-1.3089969389957492,2.5881904510251879,-9.6592582628906882,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"qx","v":{"$error":"#NUM!"}},{"$f":"qy","v":{"$error":"#NUM!"}},"TANQT",{"$f":"-1/AD44","v":-11.823551673363246},null,{"$f":"qq_x","v":9.0860103807858099},{"$f":"qq_y","v":-0.69290599360335747},"PARALLEL TO TANGEN2",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-115.1999999999999,-2.010619298297466,-21.137711904489244,10.625540865786061,null,null,null,null,null,null,null,null,-2.010619298297466,10.598148032533619,-2.5183931806010711,null,null,"If taNFR <> taNFq Then",null,null,null,null,null,null,null,null,null,"y",{"$f":"IF(vimata>3,S_3Y,YR)","v":-1.7763568394002505E-15},{"$f":"CD30","v":3.8805245642183177},{"$f":"CD32","v":"FI2"},{"$f":"CD31","v":"FI1"},null,"LINE SPT'",{"$f":"IF(vimata>3,S_3X,XR+1000)","v":-10.295630140986898},{"$f":"IF(vimata>3,S_3Y,ry+1000)","v":-1.7763568394002505E-15}]
[-0.40840704496667163,8.259791631155835,-1.9857394531738961,9.8065427818383419,-2.1636932112371206,-3.8946477802268173,5.4480793232435234,null,-1.2566370614359192,3.0901699437494559,-9.5105651629515418,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"TAN(pst)","v":{"$error":"#NAME?"}},null,null,null,null,null,null,null,{"$f":"-Ahyp","v":-9.6371213179447413},{"$f":"BHYP*SQRT(2)","v":8.5876780676484348},null,null,{"$f":"AI46*COS(phi)+AJ46*COS(psi)","v":-5.2307563230643801},{"$f":"AI46*SIN(phi)+AJ46*SIN(psi)","v":5.7831388512309347},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-111.59999999999991,-1.94778744522567,-24.448247024992956,12.628558447236591,null,null,null,null,null,null,null,null,-1.94778744522567,10.758610521472185,-2.5878315001959895,null,null,"xe = SCB / (taNFR - taNFq): YE = YB + taNFq * (xe - Bx)",null,null,null,null,null,null,null,null,null,null,null,null,null,"TANTQ",{"$f":"(t_3y-YQ)/(t_3x-XQ)","v":2.7963830820401894},{"$f":"S_3Y-t_3y++t_3x*CK46-S_3X*CK47","v":20.984007667532453},{"$f":"IF(vimata>3,CL46/(CK46-CK47),XR+1000)","v":6.6531668740452847},{"$f":"IF(vimata>3,t_3y+CK46*(CM46-t_3x),ry+1000)","v":-6.0609710893640036}]
[-0.37699111843077371,8.367988372994267,-1.8406227634233829,9.6797457632002253,-1.9796400439885977,-3.5633520791794759,5.3776365351112361,null,-1.2042771838760893,3.5836794954529854,-9.3358042649720243,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"eh",null,{"$f":"TANHP","v":8.4576955184528485E-2},null,null,null,null,{"$f":"Ahyp","v":9.6371213179447413},{"$f":"AJ46","v":8.5876780676484348},null,null,{"$f":"AI47*COS(phi)+AJ47*COS(psi)","v":13.750667258198039},{"$f":"AI47*SIN(phi)+AJ47*SIN(psi)","v":9.1300759608633957},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-107.9999999999999,-1.8849555921538741,-29.124611797498272,15.388417685876362,null,null,null,null,null,null,null,null,-1.8849555921538741,10.923116442505609,-2.6470572760834434,null,null,null,null,null,null,null,null,null,{"$f":"rx","v":8.0907117906312092},{"$f":"ry","v":-0.7770853178580881},null,null,null,null,null,"KATH FROM S",{"$f":"-1/CK46","v":-0.3576047954311104}]
[-0.34557519189487579,8.4679269205880345,-1.69368960122645,9.5655053190250197,-1.8001107654787749,-3.2401993778617948,5.3141696216805672,null,-1.1519173063162593,4.0673664307579855,-9.1354545764260173,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Ex",{"$f":"-CCC*TANHP/(TANHP-TAN(psi))","v":0.52272979387099561},{"$f":"TANHP*(AB48+CCC)","v":0.91498394338058331},"XX_1",null,null,null,"PARALLE TO TANGENT 4",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-104.39999999999989,-1.8221237390820781,-36.189650100383979,19.473714274649453,null,null,null,null,null,null,null,null,-1.8221237390820781,11.091016565919178,-2.6958367711836875,null,null,null,null,null,null,null,null,null,{"$f":"r_3x","v":11.392517092150694},null,null,null,"LINE ER",null,null,"LINE  PP;",null,null,"R'=RTT_X"]
[-0.31415926535897787,8.5595086466563863,-1.5450849718747304,9.4631600181444018,-1.6245984811645235,-2.9242772660961425,5.2573111211913339,null,-1.0995574287564294,4.5399049973954524,-8.9100652418836859,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"-CCC","v":-10.295630140987001},0,null,null,null,null,null,{"$f":"-Ahyp","v":-9.6371213179447413},{"$f":"-BHYP*SQRT(2)","v":-8.5876780676484348},null,null,{"$f":"AI49*COS(phi)+AJ49*COS(psi)","v":-13.750667258198039},{"$f":"AI49*SIN(phi)+AJ49*SIN(psi)","v":-9.1300759608633957},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-100.79999999999988,-1.7592918860102822,-48.030402710632643,26.210917905566173,null,null,null,null,null,null,null,null,-1.7592918860102822,11.261648266632045,-2.7339774751147936,null,null,null,null,null,null,null,null,null,null,null,null,null,"ER\"",{"$f":"IF(vimata>2,XE,E_3X+1000)","v":4.9912223326776477},{"$f":"IF(vimata>2,YE,E_3Y+1000)","v":1.758322218241398},null,{"$f":"IF(vimata>2,xp,xp+1000)","v":14.478532294194448},{"$f":"IF(vimata>3,yp_,yp_+1000)","v":-6.3007910877516959}]
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[{"$f":"A61+PI()/100","v":9.424777960769519E-2},8.9600576814277186,0.47054156659257851,9.0401203742131759,0.47263915589641725,0.85075048061355107,5.0222890967850979,null,-0.41887902047864112,9.1354545764260013,-4.0673664307580202,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,"pv",{"$f":"PX","v":9.4907117906312095},{"$f":"PY","v":1.6734685548162302},"QX","TANQR",{"$f":"(qy-ry)/(qx-rx)","v":{"$error":"#NUM!"}},null,null,null,"Diakrinoysa",{"$f":"b^2-GEO*a","v":53776.29918500995},null,null,"qq_x","qq_y",null,null,null,null,"Ax = PerPrxP2: aY = yp + TanpRpp * (Ax - xp)",null,null,null,null,null,null,null,null,-53.999999999999829,-0.94247779607693494,15.311714550336655,-6.8819096023558233,null,null,null,null,null,null,null,null,-0.94247779607693494,13.419062541307344,-2.2517382501445145,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"tanvT",{"$f":"-1/CI61","v":2.7963830820401911},{"$f":"t_3y-YE+CI61*XE-CI62*t_3x","v":-28.208981637404239},{"$f":"IF(vimata>2,CJ62/(CI61-CI62),xp+1000)","v":8.9439093405839891},{"$f":"IF(vimata>2,v_3y+CI62*(CK62-v_3x),yp_+1000)","v":0.34482238937584375},"TANQB",{"$f":"-1/tanfp","v":1.40998843732947},null,{"$f":"IF(vimata>3,S_3X,xp)","v":-10.295630140986898},{"$f":"IF(vimata>3,S_3Y,yp_)","v":-1.7763568394002505E-15}]
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[0.15707963267949104,8.8891950653562386,0.7821723252011612,9.1121861320920274,0.79192220162268856,1.4254599629208395,5.0623256289400151,null,-0.31415926535898131,9.5105651629515293,-3.0901699437494932,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"T  ~ PRCH= PRQ~ PH·QT where QTꓕ HP ",null,null,null,"PQH",null,null,null,null,null,"RQ",null,null,null,null,{"$f":"(-b+SQRT(Diakrinoysa))/a","v":-9.9059315274946922},{"$f":"BBB*SQRT((qq_x/AAA)^2-1)","v":0.69290599360335747},{"$f":"-AQ64","v":-0.69290599360335747},{"$f":"(AQ64--ry)/(AP64-rx)","v":4.6775013966047045E-3},{"$f":"(AR64-ry)/(AP64-rx)","v":-4.6775013966047045E-3},{"$f":"TAN(psi)","v":1.7503956233387989},null,null,null,null,null,null,null,null,null,-46.799999999999834,-0.81681408993334326,13.147378642102577,-5.3244592016239274,null,null,null,null,null,null,null,null,-0.81681408993334326,13.688366473131348,-2.0289506624064311,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Z'T"]
[0.18849555921538896,8.8405852565581959,0.93690657292862989,9.162289333719384,0.95380101109284088,1.7168418199671136,5.0901607409552136,null,-0.26179938779915141,9.6592582628906776,-2.5881904510252269,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Since HC=DS and CE1//HI  SI=HS",null,null,null,{"$f":"PX","v":9.4907117906312095},{"$f":"PY","v":1.6734685548162302},null,null,null,null,{"$f":"qq_x","v":9.0860103807858099},{"$f":"qq_y","v":-0.69290599360335747},null,null,null,{"$f":"(-b-SQRT(Diakrinoysa))/a","v":9.0860103807858099},{"$f":"BBB*SQRT((qq_x/AAA)^2-1)","v":0.69290599360335747},{"$f":"-AQ65","v":-0.69290599360335747},{"$f":"(AQ65--ry)/(AP65-rx)","v":-8.4576955184529054E-2},{"$f":"(AR65-ry)/(AP65-rx)","v":8.4576955184529054E-2},{"$f":"TAN(psi)","v":1.7503956233387989},null,null,null,null,null,null,{"$f":"ddd_2_2","v":30},null,null,-43.199999999999832,-0.75398223686154742,12.34621033258423,-4.6953125290874338,null,null,null,null,null,null,null,null,-0.75398223686154742,13.811998771873476,-1.9053183636643019,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"E_3X","v":5.9003062568096052}]
[0.21991148575128688,8.7832508574487242,1.0907162069827194,9.2220979811031061,1.1176324144857526,2.0117383460743548,5.1233877672795032,null,-0.20943951023932153,9.7814760073380533,-2.0791169081776131,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PI=SI-SP=PH (from Hyperbola definition)",null,null,null,{"$f":"qq_x","v":9.0860103807858099},{"$f":"qq_y","v":-0.69290599360335747},null,null,null,null,{"$f":"rx","v":8.0907117906312092},{"$f":"ry","v":-0.7770853178580881},null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"kk","v":45},{"$f":"ddd_2","v":30},null,null,-39.599999999999831,-0.69115038378975158,11.680526044662516,-4.1363597298623533,null,null,null,null,null,null,null,null,-0.69115038378975158,13.927624174246528,-1.7741670887540062]
[0.2513274122871848,8.7172484501576761,1.2434494358242805,9.2919228427560618,1.2837818018386411,2.3108072433095539,5.1621793570867016,null,-0.15707963267949165,9.876883405951375,-1.5643446504023284,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PE=PE1=a","y=qy+tan(psi)*(x-qx)",null,null,{"$f":"-CCC","v":-10.295630140987001},0,null,null,null,null,null,null,null,{"$f":"(PY)/(PX+CCC)","v":8.4576955184528485E-2},{"$f":"TANHP","v":8.4576955184528485E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-35.999999999999837,-0.62831853071795574,11.124611797498083,-3.6327126400267824,null,null,null,null,null,null,null,null,-0.62831853071795574,14.034786359611559,-1.6360144318402976,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"t\"t",{"$f":"IF(vimata>2,t_3x,t_3x+1000)","v":8.1679194994693738},{"$f":"IF(vimata>2,t_3y,t_3y+1000)","v":-1.8251424741521207},null,"T\"T'",{"$f":"IF(vimata>3,TTTX,xp)","v":7.8146588510944168},{"$f":"IF(vimata>3,TTTY,yp_)","v":-2.8129945748184007}]
[0.28274333882308272,8.6426431710924838,1.3949555301961527,9.372132852936133,1.4526342836595896,2.6147417105872615,5.2067404738534071,null,-0.10471975511966178,9.9452189536827316,-1.0452846326765548,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"We draw  QTꓕ HP and QX//CD to HP",null,null,"y=tanhp*(x+ccc)",{"$f":"PX","v":9.4907117906312095},{"$f":"PY","v":1.6734685548162302},null,null,null,null,null,null,{"$f":"ry","v":-0.7770853178580881},null,"gonia",null,"gonia",{"$f":"BI19","v":1.7453292519943295E-2},null,"kin energy","VELOCITY1","TAN","perp","perp1",null,null,null,null,null,null,-32.399999999999835,-0.5654866776461599,10.659365547632245,-3.1730964877207199,null,null,null,null,null,null,null,null,-0.5654866776461599,14.133062407780676,-1.4914056183440685,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"TTTX","v":7.8146588510944168},{"$f":"TTTY","v":-2.8129945748184007},null,null,{"$f":"IF(vimata>3,TTT_X,xp)","v":6.6531668740452847},{"$f":"IF(vimata>3,TTT_Y,yp_)","v":-6.0609710893640036}]
[0.31415926535898064,8.5595086466563792,1.5450849718747435,9.4631600181444089,1.6245984811645389,2.92427726609617,5.2573111211913384,null,-5.2359877559831895E-2,9.9862953475457381,-0.52335956242945836,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"∆QTS similar to ∆PEF  so  QT/QX =PF/PE=PF/a",null,null,null,null,null,null,null,null,null,null,null,{"$f":"rx","v":8.0907117906312092},null,null,null,"X1Y1",{"$f":"ABS(AAA/COS(AR68))","v":9.0013709523951686},{"$f":"BBB*TAN(AR68)","v":8.727532464108792E-2},{"$f":"kinitiki_en","v":250.28227343336766},{"$f":"AR77","v":3.3352146253335122},{"$f":"BBB/(AAA*(SIN(AR68)))","v":31.832604721416768},{"$f":"ATAN(AV71)","v":-3.1404003850152025E-2},{"$f":"AR69","v":9.0013709523951686},{"$f":"AS69","v":8.727532464108792E-2},{"$f":"AX70-AX69","v":13.485732439570027},{"$f":"AU69*COS(AV70)","v":0.10472187796836971},{"$f":"AU69*SIN(AV70)","v":3.3335701470515571},null,null,-28.799999999999837,-0.50265482457436406,10.270377032330154,-2.7487732609638318,null,null,null,null,null,null,null,null,-0.50265482457436406,14.222064468089815,-1.3409113531867061]
[0.34557519189487856,8.4679269205880257,1.6936896012264628,9.5655053190250303,1.8001107654787905,3.2401993778618228,5.3141696216805725,null,-2.0122792321330962E-15,10,-2.0122792321330962E-14,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"GP·GP/PC²=QX²/DC²   QR∙PC=QV²∙PC²/CD² and since QV²=QT²∙PC²/PF²",null,"CV²/PC²-QV²/CD²=1  ",null,null,null,null,null,null,null,null,"x*(tanhp-tan(psi))=yq-qx*tan(psi)-ccc*tanhp",null,null,null,null,"X2Y2",{"$f":"AR69+SIGN(AS69)*AU69*COS(AV70)","v":9.1060928303635382},{"$f":"AS69+(AV69)*(AR70-AR69)","v":3.4208454716926413},{"$f":"AT69+SIGN(AU69)*AW69*COS(gonia)","v":250.25087421249941},{"$f":"SIGN(AR70-AR69)","v":1},{"$f":"ATAN(AV69)","v":1.5393923229447446},{"$f":"ATAN(AV69)","v":1.5393923229447446},{"$f":"AX69+SIGN(AX69)*1/AU69*kk*COS(ATAN(AV71))","v":22.487103391965196},{"$f":"yshmeio+AV71*(AX70-xshmeio)","v":-0.33636994591061509},{"$f":"(AX70-AX69)*(AR70-AR69)+(AY70-AY69)*(AS70-AS69)","v":0},{"$f":"1/AU69*1*COS(AW69)*ddd_2","v":8.9904882930466847},{"$f":"1/AU69*1*SIN(AW69)*ddd_2","v":-0.28243018036780199},null,null,-25.199999999999839,-0.43982297150256822,9.9466522088075831,-2.3528214060612402,null,null,null,null,null,null,null,null,-0.43982297150256822,14.301441290068107,-1.1851255684784967]
[0.37699111843077648,8.3679883729942581,1.8406227634233958,9.6797457632002359,1.9796400439886139,3.5633520791795048,5.3776365351112414,null,5.2359877559827871E-2,9.9862953475457399,0.52335956242941817,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Since PVQR is a parallelogram, PV= QR. And VG→2∙PC. And  VG =2 PC in the limit. or QR∙2PC/QV² = PC²/CD²",null,null,null,null,null,null,null,null,null,"xx",{"$f":"(qq_y-qq_x*TAN(psi)-CCC*TANHP)/(TANHP-TAN(psi))","v":10.48601038078581},{"$f":"TANHP*(AL71+CCC)","v":1.7576478790709602},null,null,null,"X3Y3",{"$f":"AR70+AX72","v":9.3309301258971189},{"$f":"AS70+AY72","v":3.0900159226237212},{"$f":"AT70+BE11","v":250.25087421249941},{"$f":"SIGN(AS70-AS69)","v":1},{"$f":"-1/AV69","v":-3.1414331587110322E-2},{"$f":"TAN(AW69)","v":-3.1414331587110322E-2},"x","y",{"$f":"$CD$20","v":-8.0494531323661764},{"$f":"BA70*BA69","v":0.94150081790049145},{"$f":"BB70*BB69","v":-0.94150081790049145},null,null,-21.599999999999838,-0.37699111843077238,9.67974576320022,-1.9796400439885899,null,null,null,null,null,null,null,null,-0.37699111843077238,14.370879609663024,-1.0246630795399287]
[0.4084070449666744,8.2597916311558244,1.985739453173909,9.8065427818383544,2.1636932112371374,3.8946477802268471,5.4480793232435296,null,0.10471975511965775,9.9452189536827351,1.0452846326765146,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"QR∙PC=QV²∙PC²/CD² and since QV²=QT²∙PC²/PF²",null,null,null,null,null,null,null,null,null,null,{"$f":"qq_x","v":9.0860103807858099},{"$f":"qq_y","v":-0.69290599360335747},null,null,null,"X4Y4",{"$f":"AR70+AX73","v":8.8609337772277339},{"$f":"AS70+AY73","v":3.1047805437655525},{"$f":"AT70+BE12","v":250.25087421249941},{"$f":"-AV70","v":-1.5393923229447446},{"$f":"-AU70*DAA*COS(PI()/5)","v":-0.32360679774997902},{"$f":"-AU71*DAA*SIN(PI()/5)","v":-0.23511410091698925},{"$f":"AV72*COS(AU72)+AW72*SIN(AU72)","v":0.22483729553358153},{"$f":"-AV72*SIN(AU72)+AW72*COS(AU72)","v":-0.33082954906892004},{"$f":"Thesis(AR69,AS69,AAA,BBB,fi_1,MASS,+ENERGIAPS,ENERGELXI,ENERELAST,STATHAPOSI,STATHELXI,STATHAPOSI,2)","v":{"$error":"#VALUE!"}},null,null,null,null,-17.99999999999984,-0.31415926535897654,9.4631600181443964,-1.6245984811645162,null,null,null,null,null,null,null,null,-0.31415926535897654,14.430105385550478,-0.86015715850650487]
[0.43982297150257232,{"$f":"AAA*COS(A73)","v":8.1434434721941713},{"$f":"BBB*SIN(A73)","v":2.1288964578253693},9.9466522088076026,2.3528214060612651,4.2350785309102772,5.525917893782001,null,0.15707963267948763,9.8768834059513804,1.5643446504022887,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"QR∙PC= QT²∙PC²/PF² ∙ PC²/CD²   so 2∙QR/( QT²∙PC²)=PC/( PF² ∙ CD²)",null,null,null,null,null,null,null,null,null,"oxx",{"$f":"xxx","v":10.48601038078581},{"$f":"xxy","v":1.7576478790709602},null,null,null,"X5Y5",{"$f":"AR70","v":9.1060928303635382},{"$f":"AS70","v":3.4208454716926413},null,null,{"$f":"AV72","v":-0.32360679774997902},{"$f":"-AW72","v":0.23511410091698925},{"$f":"AV73*COS(AU72)+AW73*SIN(AU72)","v":-0.24515905313580447},{"$f":"-AV73*SIN(AU72)+AW73*COS(AU72)","v":-0.31606492792708885},null,null,null,null,null,-14.399999999999842,-0.2513274122871807,9.2919228427560512,-1.2837818018386191,null,null,null,null,null,null,null,null,-0.2513274122871807,14.478884880650723,-0.69225703509293712]
[0.47123889803847024,8.0190587176953052,2.2699524986977395,10.100936138709253,2.5476272474721515,4.5857290454498729,5.6116311881718071,null,0.20943951023931751,9.7814760073380604,2.0791169081775736,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     F⌐QR/(PH²∙QT²)=    1/(2∙CA²∙PB²)∙CP = a constant X CP.",null,null,null,null,null,null,null,null,null,null,{"$f":"PX","v":9.4907117906312095},{"$f":"PY","v":1.6734685548162302},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"CCC","v":10.295630140987001},null,null,null,null,-10.799999999999843,-0.18849555921538483,9.1622893337193769,-0.95380101109281945,null,null,null,null,null,null,null,null,-0.18849555921538483,14.517025584581827,-0.52162533438006919]
[0.50265482457436816,7.8867601203947668,2.4087683705085818,{"$f":"IF(ABS(COS(A75))>0.0000000001,AAA/COS(A75),D74)","v":10.270377032330178},{"$f":"IF(ABS(COS(A75))>0.0000000001,BBB*TAN(A75),E74)","v":2.7487732609638584},{"$f":"IF(ABS(COS(A75))>0.001,AAA*TAN(A75),F74)","v":4.947791869734945},{"$f":"IF(ABS(COS($A75))>0.0001,BBB/COS(A75),G74)","v":5.7057650179612098},null,0.26179938779914741,{"$f":"10*COS($I75)","v":9.6592582628906882},{"$f":"10*SIN($I75)","v":2.5881904510251879},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"pot",{"$f":"IF(EPILOGI=1,-stathe/SQRT((xshmeio-CCC)^2+(yshmeio)^2),IF(EPILOGI=2,stathe/SQRT((xshmeio+CCC)^2+(yshmeio)^2),-stathe*(xshmeio^2+yshmeio^2)/2))","v":3472.9311519442927},null,null,null,null,null,null,null,{"$f":"S_3X","v":-10.295630140986898},null,null,null,null,-7.1999999999998412,-0.12566370614358896,9.0715317372836726,-0.63164689223052684,null,null,null,null,null,null,null,null,-0.12566370614358896,14.544376973410209,-0.34893546173640572]
[0.53407075111026614,7.746678243035487,2.5452070787518624,10.456094529654901,2.9569917569973643,5.3225851625952556,5.808941405363834,null,{"$f":"I75+PI()/60","v":0.31415926535897731},9.5105651629515418,3.090169943749455,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"kin_energ",{"$f":"energia-AR75","v":250.28227343336766},null,{"$f":"AT70","v":250.25087421249941},{"$f":"AU70","v":1},null,null,null,"r","polar",{"$f":"1.3","v":1.3},null,null,null,-3.5999999999998411,-6.2831853071793092E-2,9.0177945576402774,-0.31457333626823486,null,null,null,null,null,null,null,null,-6.2831853071793092E-2,14.560831103699822,-0.174868945194773]
[0.56548667764616412,7.5989513295181297,2.6791339748949889,10.659365547632271,3.1730964877207497,5.7115736778973494,5.9218697486845953,null,0.36651914291880722,9.3358042649720243,3.5836794954529845,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"velocity",{"$f":"SQRT(2*AR76/MASS)/SMIK","v":3.3352146253335122},null,null,null,null,null,null,{"$f":"SQRT((xshmeio-S_3X)^2+(yshmeio-S_3Y)^2)","v":19.297198454187068},{"$f":"polar*ar","v":25.08635799044319},null,null,null,null,1.5902773407317584E-13,2.7755575615628914E-15,9,1.3877787807814457E-14,null,null,null,null,null,null,null,null,2.7755575615628914E-15,14.56632303851559,-1.1274577253394212E-4]
[0.59690260418206209,7.4437251684710493,2.8104168892606585,10.88164839065888,3.397996491122643,6.1163936840207569,6.0453602170327114,null,0.41887902047863712,9.1354545764260173,4.0673664307579838,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"1)      If the body is on P, we draw the conjugate diameters GP and DK and the line joining the focus S with P and the tangent RZ on P",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"tanar",{"$f":"(yshmeio-S_3Y)/(xshmeio-S_3X)","v":4.5227403065764915E-3},null,null,null,null,3.6000000000001595,6.2831853071798643E-2,9.0177945576402809,0.31457333626826278,null,null,null,null,null,null,null,null,6.2831853071798643E-2,14.560831103699821,0.17464345364970507]
[0.62831853071796007,7.2811529493745191,2.9389262614623712,11.124611797498119,3.6327126400268153,6.5388827520482673,6.1803398874989552,null,0.47123889803846702,8.9100652418836876,4.5399049973954506,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2)      QR deviation from inertial motion. Deviation =QR = 1/2∙(F/m)∙t².       F~QR/t²",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"FORCECONST","v":-363.71923023977314},null,"FORCE",null,null,"METROD",null,null,"rplu",{"$f":"S_3X","v":-10.295630140986898},{"$f":"S_3X+polar*ar*COS(ATAN(tanar))","v":14.790471280409786},null,null,null,null,7.20000000000016,0.12566370614359451,9.0715317372836797,0.63164689223055503,null,null,null,null,null,null,null,null,0.12566370614359451,14.544376973410207,0.34870997019133765]
[0.65973445725385804,7.1113951113812046,3.0645352682648879,11.390170104648826,3.8783975552480769,6.9811155994465386,6.3278722803604586,null,0.52359877559829693,8.6602540378443962,4.9999999999999831,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"t ~area of RHP=area of HSP ~ QT Χ HP ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(vimata>3,xshmeio,1000)","v":9.0013709523951686},{"$f":"IF(vimata>3,yshmeio,1000)","v":8.727532464108792E-2},null,{"$f":"-IF(EPILOGI=3,FORCECONST*ar,FORCECONST/ar^2)","v":0.97673721875117503},{"$f":"tanar","v":4.5227403065764915E-3},{"$f":"ATAN(AV82)","v":-1.5662736173257639},{"$f":"AR80","v":9.0013709523951686},{"$f":"S_3Y","v":-1.7763568394002505E-15},{"$f":"S_3Y+polar*ar*SIN(ATAN(tanar))","v":0.11345792203341483},null,null,null,null,10.800000000000161,0.18849555921539038,9.1622893337193858,0.95380101109284809,null,null,null,null,null,null,null,null,0.18849555921539038,14.517025584581825,0.52139984283500107]
[0.69115038378975602,6.9346191849820942,3.1871199487434545,11.680526044662559,4.1363597298623915,7.4454475137523044,6.4891811359236442,null,0.57595865315812678,8.386705679454252,5.4463903501502546,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"3)      Draw HI parallel to DK. Since DK conjugate to PG, RZ parallel to DK. It Is well known from optics that the RZ makes equal angle ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"MEGETHYNSY",3,{"$f":"AR80+MEGETHYNSY*SIGN(FORCECONST)*SIGN(AS80)*AU80*COS(AV81)","v":6.0711892646851435},{"$f":"AS80+(AV80)*(AR81-AR80)","v":7.4022873816489462E-2},null,{"$f":"SIGN(AR81-AR80)","v":-1},{"$f":"ATAN(AV80)","v":4.5227094691327871E-3},{"$f":"ATAN(AV80)","v":4.5227094691327871E-3},{"$f":"AX80+SIGN(AX80)*1/AU80*kk*COS(ATAN(AV82))","v":9.2097394146260783},null,null,null,null,null,null,14.40000000000016,0.25132741228718625,9.2919228427560654,1.2837818018386487,null,null,null,null,null,null,null,null,0.25132741228718625,14.478884880650718,0.69203154354786878]
[0.72256631032565399,6.7509996266741261,3.3065593266182653,11.998223149051569,4.4080929618159592,7.9345673312687266,6.6656795272508713,null,0.62831853071795662,8.0901699437494852,5.8778525229247149,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," (so SP reflected to PH) perpendicular PF to DC is DFꞱHI so PH=PI. From Thales Since CH=CS then CH/CS=SM/MI so SM=EI",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AR81+AX83","v":6.3937294036228494},{"$f":"AS81+AY83","v":0.31059814465865765},null,{"$f":"SIGN(AS81-AS80)","v":-1},{"$f":"-1/AV80","v":-221.10489044571176},{"$f":"TAN(AW80)","v":-221.10489044571347},"x","y",null,null,null,null,null,18.00000000000016,0.31415926535898209,9.4631600181444124,1.6245984811645471,null,null,null,null,null,null,null,null,0.31415926535898209,14.430105385550473,0.85993166696143608]
[0.75398223686155197,6.5607176467926944,3.4227355296434494,12.346210332584283,4.6953125290874773,8.4515625523574585,6.8590057403246014,null,0.68067840827778647,7.7714596145697215,6.2932039104983586,null,null,null,null,null,null,null,null,null,null," ",null,null,null,null,"4)      Since MI=HE then PE=(PH-HE)=(PI-PM)=(SI-PM-SP)=2a -SM=2a-(2a)/2=a",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AR81+AX84","v":6.3958561019136866},{"$f":"AS81+AY84","v":-0.15962524794787419},{"$f":"SIGN(AS82-AS80)","v":1},{"$f":"-AV81","v":-4.5227094691327871E-3},{"$f":"-AU81*DAA*COS(PI()/5)","v":0.32360679774997902},{"$f":"-AU82*DAA*SIN(PI()/5)","v":0.23511410091698925},{"$f":"AV83*COS(AU83)+AW83*SIN(AU83)","v":0.32254013893770617},{"$f":"-AV83*SIN(AU83)+AW83*COS(AU83)","v":0.2365752708421682},null,null,null,null,null,21.600000000000158,0.37699111843077793,9.6797457632002413,1.9796400439886221,null,null,null,null,null,null,null,null,0.37699111843077793,14.370879609663019,1.02443758799486]
[0.78539816339744994,6.3639610306789169,3.5355339059327435,12.727922061357877,5.0000000000000169,9.0000000000000302,7.0710678118654871,null,0.73303828583761632,7.4314482547739571,6.6913060635885664,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"5)      ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AR81","v":6.0711892646851435},{"$f":"AS81","v":7.4022873816489462E-2},{"$f":"-AU82","v":1},null,{"$f":"AV83","v":0.32360679774997902},{"$f":"-AW83","v":-0.23511410091698925},{"$f":"AV84*COS(AU83)+AW84*SIN(AU83)","v":0.32466683722854284},{"$f":"-AV84*SIN(AU83)+AW84*COS(AU83)","v":-0.23364812176436364},null,null,null,null,null,25.200000000000156,0.43982297150257377,9.9466522088076097,2.352821406061274,null,null,null,null,null,null,null,null,0.43982297150257377,14.3014412900681,1.1849000769334275]
[0.81681408993334792,6.1609239533581874,3.6448431371070633,13.147378642102641,5.324459201623978,9.5840265629231602,7.3040992456125782,null,0.78539816339744617,7.0710678118654897,7.0710678118654604,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," (SEE APPENDIX)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,28.800000000000153,0.50265482457436961,{"$f":"IF(ABS(COS($BF85))>0.0000000001,AAA/COS($BF85),\"\")","v":10.270377032330186},2.7487732609638678,null,null,null,null,null,null,null,null,0.50265482457436961,14.222064468089807,1.3406858616416364]
[0.8482300164692459,5.9518067879128553,3.7505553481523037,13.609312749281063,5.6713867462770473,10.208496143298685,7.5607293051561468,null,0.83775804095727602,6.6913060635885984,7.4314482547739278,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"6)      From QRPX rectangle QR/PV=PX/PV=PE/PC=AC/PC",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,32.400000000000155,0.56548667764616545,10.659365547632282,3.173096487720759,null,null,null,null,null,null,null,null,0.56548667764616545,14.133062407780667,1.4911801267989981]
[0.87964594300514387,5.7368159077381948,3.8525662138789518,14.119330531548323,6.0439617520480668,10.879131153686521,7.844072517526846,null,0.89011791851710587,6.2932039104983915,7.7714596145696948,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"7)      QT/QX=PF/PE   QT²=QX²·PF²/AC² = in the limit t→0 GV=2PC  and",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,36.000000000000149,0.62831853071796129,11.124611797498128,3.6327126400268246,null,null,null,null,null,null,null,null,0.62831853071796129,14.034786359611548,1.6357889402952266]
[0.91106186954104185,5.5161634828767756,3.9507750618784576,14.684118817623782,6.4459611589253569,11.602730086065643,8.1578437875687673,null,0.94247779607693571,5.8778525229247496,8.0901699437494621,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," PV=QR PC/AC",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,39.600000000000151,0.69115038378975713,11.680526044662569,4.1363597298624004,null,null,null,null,null,null,null,null,0.69115038378975713,13.927624174246517,1.773941597208935]
[0.94247779607693982,5.2900672706322442,4.0450849718747426,15.31171455033676,6.8819096023558943,12.38743728424061,8.506508083520421,null,0.99483767363676556,5.4463903501502902,8.386705679454229,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"QX²=QV²=2PC· PV·DC²/PC²= 2PV·DC²/PC or since PF·DC=BC·AC  and",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,43.200000000000152,0.75398223686155297,12.346210332584294,4.6953125290874862,null,null,null,null,null,null,null,null,0.75398223686155297,13.811998771873466,1.90509287211923]
[0.9738937226128378,5.0587504006691617,4.1354028713728148,16.011859369318852,7.3572765790998753,13.243097842379775,8.8954774273993618,null,1.0471975511965954,5.0000000000000195,8.6602540378443749,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"QT²=QX²·PF²/AC²= 2PC· PV·DC²/PC²·PF²/AC=2QR·PC/AC ·BC²·AC/PC=2QR·BC²",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,46.800000000000146,0.81681408993334881,13.147378642102654,5.3244592016239869,null,null,null,null,null,null,null,null,0.81681408993334881,13.688366473131337,2.0287251708613585]
[1.0053096491487357,4.8224411548109556,4.22163962751008,16.796472450305156,7.8787392998432875,14.181730739717917,9.3313735835028648,null,1.0995574287564254,4.5399049973954879,8.9100652418836681,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,50.400000000000148,0.87964594300514465,14.119330531548336,{"$f":"IF(ABS(COS($BF91))>0.0000000001,BBB*TAN($BF91),\"\")","v":6.0439617520480766},null,null,null,null,null,null,null,null,0.87964594300514465,{"$f":"x_ken+r_cakmp*COS($BQ91)","v":13.557215198221041},{"$f":"y_ken+r_cakmp*SIN(BQ91)","v":2.1443505732344099}]
[1.0367255756846336,4.5813727417533272,4.3037101350197231,17.680290289805292,8.4545382789250922,15.218168902065166,9.8223834943362736,null,1.1519173063162553,4.067366430758022,9.1354545764259996,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"         Q.O.D.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"DEGREES(BF92)","v":54.000000000000149},0.94247779607694049,15.31171455033677,6.8819096023559041,null,null,null,null,null,null,null,null,0.94247779607694049,13.419062541307333,2.2515127585994401]
[1.0681415022205316,4.3357830669154227,4.3815334002193227,18.681746468839201,9.0949662364053729,16.370939225529671,10.378748038244002,null,1.2042771838760853,3.5836794954530227,9.3358042649720101,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,57.600000000000144,{"$f":"BF92+PI()/50","v":1.0053096491487363},16.796472450305174,7.878739299843299,null,null,null,null,null,null,null,null,{"$f":"BQ92+PI()/50","v":1.0053096491487363},13.274453727811103,2.3497888067685584]
[1.0995574287564296,4.0859144976559056,4.4550326209418438,19.824203381267477,9.8130525275258016,17.663494549546442,11.013446322926375,null,1.2566370614359152,3.0901699437494941,9.5105651629515293,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,61.200000000000152,1.0681415022205323,18.681746468839226,9.0949662364053871,null,null,null,null,null,null,null,null,1.0681415022205323,13.12395946265374,2.4387908670776968]
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