Philosophiae naturalis principia mathematica . tionemConicam per pun&a C, Z>, P tranfeuntem, & reclam B H tan-gentem in pun&o B. QJL; F. Cas. 2. Dentur pun&a quatuor £, C, D, P extra tangentemHI fita. Jungebina B D, CP coneurrentia in G, tangentiq; oc-currentia in H & I. Se-cetur tangens in A, ita utfizHAzdAI, uteftreft-angulum fub media pro-portionali inter B H & H-D & media proportionaliinterCG&GP, ad re&*angulum fub media pro-portionali interPI <kIC& media proportionali in*ter D G & G B, & erit Apunctum contaftus. Namfireclse Plparallela HX trajecroriam fecet in pun&is quibufvis X & Y
Philosophiae naturalis principia mathematica . tionemConicam per pun&a C, Z>, P tranfeuntem, & reclam B H tan-gentem in pun&o B. QJL; F. Cas. 2. Dentur pun&a quatuor £, C, D, P extra tangentemHI fita. Jungebina B D, CP coneurrentia in G, tangentiq; oc-currentia in H & I. Se-cetur tangens in A, ita utfizHAzdAI, uteftreft-angulum fub media pro-portionali inter B H & H-D & media proportionaliinterCG&GP, ad re&*angulum fub media pro-portionali interPI <kIC& media proportionali in*ter D G & G B, & erit Apunctum contaftus. Namfireclse Plparallela HX trajecroriam fecet in pun&is quibufvis X & Yi erit ( ex Conicis)UAquad. zdAIquad. ut reftangulum XHTad re&angulumB HD C feurcclangulum CGPad re&angulum DGB ) & recl-angulum £ H D ad re&angulum PIC conjunctini. Invento autemconta&us punclo A, defcribetur Trajecloria ut in cafu F. Capi autem poteft puncrum A vel inter puncia H & I,velextra; & perinde Trajectoria dupliciter defcribi. M 2 [84] Prop. XXIV. Prob. XVI. Traje&oriam defcribere qu reffias duas pojitione datas tangentes HI, K L & pun&a B, C, D. AgeBDtangentibus occurrentem in pun&is H, JC, &: C D tangentibusoccurrentem in pundisZ, L. AdTas itafeca in R & S,ut K R ut eft media propor-tionalis inter B H & H D admediam proportionalem in-ter Btf & K£>; & IS adLS ut eft media proportio-nalis inter CI & JJ) ad me-diam proportionalem interCLSlLD. AgeRS fecan-tem tangentes in A & P, Scerunt ASc P puncTa contac- 5;. ;..---tus. Nam fi per puncTorumH, J, Jf, L quodvis I agaturredTa ITtangenti KL paral- Y lela & occurrens curvae in X Sc T, & in ea fumatur IZ media proportionalis inter IX & /2*:erit, ex Conicis, reclangulum XIY (feu IX ad L P ^? rectangulum C JD ad recTangulum CLD; ideft C per con-ftruclioneni J) ut SI quad. ad SL </;W. atqi, adeo JZ ad LP utS J ad S L. Jacent e
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