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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIPLA MATHIEMATICA.
L E MI M A XX.
Si Parallelorrammum quodvis ASP D’anculis duobus opposiris A 
Prancit sectionem quam vis Conicam in punctis A e P; e lateri
bus unius angulorum illorum infinite productis A Q AS, occurrit
eidem sectioni Conicae in B e C; a punctis autem occur suum B e
C ad quintum quodvis sectionis Conice punctum D acantur rec-
tae duae BD. CD occurrentes alteris duobus infinite productis pa-
ralleloerammi lateribus PS, P O in T ( R: erunt semper abscissa
laterum partes PR es PT ad invicem in data ratione. Et contra, si
partes illa abscissae sunt ad invicem in data ratione, punctum D tan:
set Sectionem Conicam per puncta quatuor A, B, C P transeuntem.
Ca5. T. TUnganEuE BF, C F ec 2 puncto D agantur rectxe dux
DO, DF, quarum prior,
DG ipA B Parallela (IE d
OCCUTTAE PB, P Q.
e
A
II, L, G; altCTa D F paral.
lcla sIE ipA AC _E OCCUEraL
FC, FS. AB in F, L, F:
ec crit (per Lemma ZVTL.) re-
etangulum D F. X D S ad re
etangulum DGX D NTin ra-
tione data. Sed est F C) ad
DF (CCu TO) uc P B ad HIB,
adeoquevc F F ad D HI; dc
vicissim P _ ad ~ T UE D F ad D HI. EA _C P R ad D F UE RC
ad D C, adcoquenE (TC vel) PS ad DG, ee vicissim F R 2d S
UE D F ad D G; ex conjunetisrationibus sic rectangulum P Q X F se
ad rectanoulum F SX F F uc rectangulum D F X D F ad rectan.
sulum DGX DEI, acque adeo in data rationc. Scd daneur P d
ec FS e propterea ratio P R ad PT datur. Q. P. D.
Ca5. 2. Ouod A P R ec P T ponantur in data ratione ad invi-
cem, cum simili ratiocinio reprediendo, sequetur esse rectangulum
DEX D F ad rectangulum D GX D H in ratione data, adeoque
punctum D (Per LemIA XVTTL.) concingere Conicam sectionem
cranscuntem per puncta , B, C, P. d. Ls. D.
Corot.
LIBEK
P R1MVS.