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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 79, page id 1041163592:0113
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eRINOIPTA MATHEMATIOA
99
ec T. D. Seca autem pro lubitu vel inter puncta I et II,. LIVEK
ec In vel exera eadem: dein asc RS secantem tangentes in A. Puruvs.
ec P, e crunt A ec P puncta contactuum. Nam sI A ec F
supponantur esse puncta contaetuum alicubi in tansentibus (i-
ta; e per punctorum II, I, K, L. quodris P, in tansente al.
cerurra AC sicum agatur recta i P tangenti alteri R L. Paral-
lela, quae occurrac curra. in X ec P, e in ea lumatur IZ me
dia proportionalis incer PX e PV: crit, ex Conicis, rectangulum
XTY CCu IZ quad. ad L. P quad. ut rectangulum C I D ad rectan-
sulum CL D, id eA (per constructionem) ut SY quad. 2d
SL quad: acque adeo TZ ad L, P ut SI ad SL. Tacent erso punc-
ta 5,F. L in una recta. Porrotangentibus concurrentibus in 6, C-
rit (ex Conicis) rectangulum XIY Ccu IZ quad. ad Y A quad. UE
GF quad 2d CA quad: adeoque 1Z ec I  uE CF 2d G . TaCCNE
ergo puncta P. L ex A in una recta, adeoque puncta 5, F et A
Tunt in una recta. Et eodem argumento probabitur quod puncta
R, F ec A Tunc in una recta. Jacent isitur puncta contactuum 
ec P in recta RS. TTisce autem inventis, Trajectoria desexibetur
uc in calu primo Problematis superioris.
Q. F. F.
L F MIM A ZXII.
Firuras in alias ejusdem reneris firuras mutare.
Transmutanda sIE Figura quaeris FTGT. Ducantur pro lubieu
rectae duxe parallelae AO, BF. terriam quamvis posirione dacam.
AB sccantes in AeEB,
ec a figurae puncto quo
vis C. ad rectam AB
ducatur quaeris (D,
ips O A Parallela. DC-
inde a puncto aliquo0.
in linea OA daco, ad
punctum D ducatur
recta O D, ipA BL OC.
currens in d, ec 2 puncto
Occursus crigatur rect.
de dacum quemris angulum cum recta B L. CBMLHCHS, aEque CaNE
hrabens rationem ad O d quam habet D C ad O D; ec crit s punc-
tum in figura nova hei puncto C respondens. Padem rarione
puncta singula figurae primae dabune puncta tocidem Agura nOvX.
pE