# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175905688X:0364
# Permalink to this reading: https://leibnizlegible.com/page/175905688X:0364?run=74
# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 342, page id 175905688X:0364
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=364
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000364.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.83
# 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.

342
PR A N CESCF A SCHOOFBN
partem rerocentur, reliquae rero ad alteram, ac demum ueraque
pars xqualitatis diridatur DeTZ L C, OFICTUESZZ =- CCZ = bZZ
2b6Z a b6C- bbZ. f bbc ∞ 2a aY
Cum vero ec supra inrentum fueric c dd L CCA = bd d - 2bc d
 bbd = bbc b6c∞ 2aaY, e, qux eidem aequaneur incer le
quoque sint ae qualia eriECZ Z = 66Z - bZ Z + 2bCZ -- bCt
bbZ = bbc∞ Cdd F c6d - bd d  2bcd + bbd + bbc- bc6.
Deleantur utrinque aequalia, e quancitates in Z Z ductae unam
partem ae quationis consticuane, reliqua rero alceram, habebitur.
que + c2Z∞. f662. c d d. UIbicandem. l urrobique dirida.
bC CC
L bb ba d
 bC
L bb
turPer C b, OrietuT ZZ DCZ F d d. IToc est, S collocentur
um b  cd
quancitates omnes ad unam partem, erit
ZZ 6Z nm d d ∞ O.
L b ca
L ba
Duare postguam percurrimus omnia propolitionis data, ea
que lic enodarimus, ut difficultas omnis reducta sic ad aequatio
neI ZZ = 62 = d d ∞ 0: superestut ipsa contineat quaelicum
Lb = cd
L bd
propolitionis, modo sic rerum atque ex datis deduci pOssit. Ad
quod explorandum, videri debet, num aequatio inrenca diridi
POAE PeT Z = C = d F b ∞0. Juare cum reperiatur divitionem
tieri posse, atque oriri Z = d ∞0, sequitur quae sicum propolitio
nis esse rerum, hoc eAt, Z F b xequaric. f d, Cive IIIRM N simul
sumpeas aequales esse iplis B C et FD simul sumpris. Ouod erut
demonstrandum.
Undeliquet, si Circulus non transiens per verticem Parsbole
camtansat in B vel F, hoc est, rectas C B, D E Sibiinricem x.
quales Faciac, eunc FII, M N simul sumptas iplius C B vel DP.
duplasfore.
Sienim in hac ulcima xquatione pro d scribatur c, crit xqua-
in