# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/834940469:0089
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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 5, page id 834940469:0089
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=834940469&page=89
# Source image: https://digitale-sammlungen.gwlb.de/content/834940469/jpgs/default/00000089.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.88
# 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.

busaequales e parallellae, a perpendicularibus proximisrer.
minaea. Angulus B9B eAt rectus oboB ransencem; ee ille
perpendicularem 96; angulus quoque 093 es rectus, de
ideo communem angulum 096 auterendo, relinquitur an-
Bulus Og Bxequalis angulo 693; triangulaisieur rectansula
09B, 693, suc similia, ee proinde ut 93 2d96 ita 90 ad 9B, (cd
uc 93 ad96 ica X ad 3NV; _ id eo uc 90 ad 9B ica X ad 3H; de
iditur rectangulum 9O in 3N nempe rectangulum Nq CA
aequale rectangulo 9B in :Codemodo demonstratur rectan.
gulum P3 esse aequale rectangulo 7 A in X, icem rectangu.
lum L.d esseaquale rectangulo CF in X: _ id eo rectangulum
rectae L inrectas7 A, 9B, C F, Simul, est aequale eori recti-
linCO ZPYNKLCS; est ergo rectangulum X in rectaS 7A,
gB, CF, Simul, maior mixeilineoP NL IIS2. curra in puncto
Dhacnormalis D=. e ideo rectus cA angulus DX, (cd
rectus quoque est angulus Ses, ee proinde commune aute-
rendonempe SDS relinguueur anguli a quales SDI, 8D5:
sunc ergo criangula rectangula sD, 8D5, limilia; d ideo
UE SD adD=, hoc est D5 ad OX ica X ad SHI, e ideore-
ctangulum SE in D5, hoc est rectansulum I4, aequale elt
rectangulo X in DX, hoc cA, X in 7r; sed rectangulum
Mq es aequale rectangulo L. S, hoc ek rectangulo X in C F
e rectansulum 23 ck equale rectangulo N4 hoc es rectan-
sulo X in gB; e igitur rectilineum ONMLIHISZ est ae quale
rectangulo Z in rectaS FC, B9, V73 Simul; est ergo rectongu.
Jum X in rectas FC, Bo, Y7. Simul, minor mixcilincOPNLHL
S2. POrrOrCCtA FCBO, A7, SimuI lunemaioreS CuTrA 7QCD,
ee rectae FC, B9, V7 simul, Cunc eadem curraminores, quod
utrumq; Parec ex ancecedenre; de igitur rectangulum X in
rectas LCB9, A7, Maius elt cylindrica superticie (uper Cur-
va79C. D, de recrangulum X in ReCEAS FC, B9rV7, eadem (u-
perticie minus: Ped demonstracum es reccangulum X in rC-
CeaS FC, B9 A7maius esse mixtilinco PHLHSZ, de rectan-
sulum Xin rectaSFC, B9, V7, eodem mixcilineo eNe minus,e
PiO.