# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/824573315:0173
# Permalink to this reading: https://leibnizlegible.com/page/824573315:0173?run=74
# 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 89, page id 824573315:0173
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=824573315&page=173
# Source image: https://digitale-sammlungen.gwlb.de/content/824573315/jpgs/default/00000173.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.85
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

PROP. 37.
De Sectionibus Conieis.
e
atq ordinatim. applicatas recte a P hyperbolam in a
concingenci parallelas.
Libet proposicionem (ut prius 24 _3F.) Analycice ex aminau
res deinde et Synchecice demonstrare.
Supponamus isitur rem esse uc perhibetur, adeoq; infcrip-
eam quamlibet OO cangenti at parallelam a recta C a (per
cenerum _ comactum cranseuncC) Bilectam in n. Sincq; re-
aa OD, OD, atI, diameero HA ordinacim applicaTZ, _ prO.
peerca inricem parallela; quibus eriam parallela ducacur nl
eidem diametro inh OCCurrens; quX propterca (propter Pa-
raltelas) bisceabic, (uEOO) in n, sic) DD in h. Denig: recta
OO (producta li opus) diametro HA OcCurraEIM O: OCcUr-
Curam enim omnino esse parec, quoniam a F ipi parallela ei-
dem diametro occurric, per praced.
Supponemus etiam impraelenciarum, occursus punctum C
concingere supra verricem A, exera Hyperbolam. Si aucem le.
cus concinsae, (uei heri porest, E inleripea OO remocius a
cangente lumatur, ita uc diametrum cranteac,) non camen le-
ries operationis variabitur alicer quam vel mucanda aliquando
Tiena t =, vel quancicarem aliquando nesacire interpretan-
dam Fore, adeogi ex parte suppolicioni concruria, incelligen.
dam.
Dicancur aurem (ob commodiorem ca lculum) H a = B,
IA = d, Aa -- 1 Ha (= 1Fd) = 2, HC (= 31 F d) = c, HD = 9.
an - s, aC = - 5, nC (= 0+ 5) - ∞, 20td C.
d2
Tum Cper praccd. ) HC. Ha: : F A. HF. HOC cRC. Z:: d.
=HF. EE Cpropeer parallelas _ Similia criansLla) C8. an
: CH. Hh. hoc eA0. s: : c. = Hh. FCCa Cn:: F0. Hn::
HF. BO. hoc cAs. 7:: B
(= hO= HD)
oeh a (= ,t at
rdZ
tn:
d2. 2d2
c 6c
=HO. ideoq. DO
ac 9. Icem HA (= AR + H B) = at
2 t - -. Ideoqs DA = dt  + 9, e