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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 55, page id 824573315:0139
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PROP, 24.
DeSectionibus Conicis.
AP (Calcem producta) in C. Coccucturam aurem cerium ett,
cum ipli parallela at cidem diametrO OccurraE, Duca in l, Der
Praecedencem) Enincq; (propior para l LC ( 28), CP= q FC:
ee propierea PF- pC5
Tam Cubstiuis Cob commodiorem estcutum) idoncis
Cymbolis, cAoPa P. PA = d. (id eoq; per praccd: PF - - pC
2d.) ep a0 EC- 8, (erBD DA DPt PA = at 5) DD = 9.
ideoq DA- DA F∞D at C = g. _ DO = DC d ∞D = 2d
59.
Eric isicur (propter Parabolam) PA. DA:: Pag. DO9. HOC
CA d. at g:: p.
1. 12
= DO9.
Icem (propeer similia criangula) PF. PA:: DC. DO. HOC
est 2d. P:: 2d 79. 2 =9p- DO. Ec C lumendo quadrata)
4d = 4d9 t 9 p. -
4d
21
et e = a p
Ergo (uerinq; diriiendo perpe e mulciplicando per 4d)
1d + 1d9t9 =4d Y4d8 =4d9. hoc eA C Tublacis uerinq. aequa-
libue) 9=4d8. Adeog; inventa cA quancicas 9, adeoq; &
puncta I, D. quibus Ordinacim applicancur DO, DO. Vera iei
tur cApropolicio.
Illud Syniherice sic demonstrabimus, premendo AnaIy (COS ve-
Rigia.
Diometro AP ducatur parallela an, per cujus punctum
quodris Cintra parabolam) x, diieatur recta nC diameero
occurrens in G, e parallela rangenei ab occurremi diamecro
in F. Dico ao ejuldem Parabolae diameerum esse eiq; ordina-
tim voni rC.
Diametro AP ordinatim axplicetur ab, elq; paralsela du-
Catur p diaMetrO OCCUErENS in P. EF sunco CymBola Pa- P.
PA --d. P(3- a N - C.
Tum Cumaneur in diametro verinq; a puncto P, aqua les re
ctx PD  (V 4de =) 2 V de. Choc est, duplum medie pTOPOr-
eionalis incer A P, a ∞, recta s.) acq; punctis D, D, ordinacim.
DONanEUE DO, DO, rectae rC Occurrences in (), C); quae cum
parallelae sint recta re, AICUC recta BD C ex constructione) bi
ECCBLIR