# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1047377675:0021
# Permalink to this reading: https://leibnizlegible.com/page/1047377675:0021?run=74
# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 5, page id 1047377675:0021
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=21
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000021.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.87
# 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.

busaquales e parallella, a perpendicularibus proximis cer-
minacae. Angulus BgSCs rectus ob gB tangencem, e ille
perpendicularem 96; angulus quoque 095CH rectIS, dE
ideo communem angulum 396 auferendo, relinquitur an
sulus OgBaequalis angulo 693; triangulaigitur rectangula
09B, 593, suc limilia, _ proinde ut 93 2d96 ita 90 ad 9B, (c d
NF 93 ad 96ica X dd 3H; _ id eo ut 9O ad 9B ica X ad 3N; &
deitur rectangulum 90 in zVI nempe rectanoulum Nq CA
aequale rectangulo oB in X: Codemodo demonstraeur rectan
sulum P3 esse aequale rectangulo7 A in X, item rectangu-
dum L.S essexquale rectangulo C. F. in X; dc id eo rectangulum
rectae X inrectas 7 A, 9B,C F, limul, est aequale toci recti-
LInEO ZPYNKLCS; eA ergo rectangulum X in rCCIS 7A,
9B, CF, Simul, maior mixcilineo P NL. IId2. currae in puncto
Bhacnormalis D e ideo rectus est angulus  DZ, sed
rectus quoque est ansulus dis, de proinde commune aute-
rendo nempe sid; relinguutur anguli ae quales SDn, D5:
Lunc ergo criansula rectansula sD, 8D5, limilia; a ideo
UE SId AaD, hoc CA _5 ad DX ita X ad stI, X ideore-
ctangulum sEI in D5, noc cs rectansulum II4, aequale clt
rectangulo Z in DX, hoc est, X in 7 V; sed rectangulum
M4 est aequile rectangulo L. S, hoc est rectangulo X in C. lis
e rectangulum s elt equale rectansulo N4. hoc est rectan-
Sulo X in gB; _ igitur rectilineum ONMLIIISZ est ae quale
rectangulo X in rectas FC, B9, V7 simul; est ergorectansu
lum X in rectaSFC, B9, V7 Simul, minor mixcilineOPNLEI
82. POrro rectae FC, B9, A9, Simul lune maiores currA 79C. D,
de rectae FC, B9, V7 simml, Cunt eadem curra minores, quod
UErumq: PACCE ex ancecedente; de isitur rectangulum X in
rectaS FC B9, A7, maius clc crlindrica luperticie luper cur
Ya7gC D_ rectangulum X in rectaS F C B9, V7, eadem su-
pertcie minus: sed demonstrarum est rectangulum X in re-
CTaS FC, B9, A7maius ese miscilincO PNLHSE, de rectan-
Bulum Rin rect AS L. C, B9, Y7. C0 dem mixrilinco cAC MInUS,e
D1S