# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068160:0045
# Permalink to this reading: https://leibnizlegible.com/page/00068160:0045?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 23r, page id 00068160:0045
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 24v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068160&page=45
# Source image: https://digitale-sammlungen.gwlb.de/content/00068160/jpgs/default/00000045.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.81
# 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.

Uela ek
 ad Q rect
iangula rep
ep, et 2C3C
t si
constructio calculo inserviens
Datur recta positione et magnitudine rectae p2C
et 1C2C 3K dantur ergo et rationes, inter
ipsas 1C1Z, aq2C, et 1C2C. rursus assumitur 2C2G
t complentur pmrilellogmanm rcrGzC
es
1t
K
mnatus r3C
et ex3C demissu perpend. in sC nempe 3C patet (ob
triang. 3k REC congruum ipsi 2C 192C) et fore 2CR = 2C1Z.
et jam 2CM = 3CK. _hC2G. Ergo 2EM = 1q2G. et 3CM = 1c1Q
Noster jam scopus est investigare 223C ex ipsis 2C2C, 192Ge
Rectanguloium i 1C2CB et 2CgCp vator Evis sit  cd, fint 1eiq co p 2C
et B2C sit p firt 1C19 = co: p P quia 1CM = _ 2G1g. fier acF
2CM seu 2G19 + MC seu co: p = 1 C3C seu 2129+ 293C = cd: p3  F 223C
rursus p2g. 2c29 e cd. PdC. peC seu p. PM seu p+9 et
(17
seu a + co: p = co: B + n et ob trangula simili. P2 q2C et pM3C
fiet F P2E seu Pn 2 e2C seu co: b: P2 C seu p ; P M seu p + G: Mde sn co. P. pres
seu b - n: co, b: p:: p +q: co: p: b
(2
Ergo b nb = p  p9 et pb pn=
et Bn = -p et b -n oco: p = co: b prq seu b -n csb = p+ 9 sp, ut ante
(quia  co: b: p:: co: p: b identica est, jam ec erZ. 1Z seu q 
Sa
m: a. Ergo 1C14 seu co p= q1v m. a. Ergo sed hoc anno lari
Recta p2C est primum assantum p. Area Trianguli est
inutile.
secundum assumtum; area Trianguli), Co (seu aco si mavis) quae est constans
les
est secundum hinc sequitur 1C1Q = co: p. Tertiam assumbum est 2C2G= ∞
Linc catera determinantur sed in aequationes 1 et 2 nondum s  aecq
nam q seu Tertium assumtum est 2CVQ se quam vocabimus _A  quartum
er
est 2C2G seu v. es Ex his caetera determinantur nam 2G18 seu q2
desideranus autem P= n= _h Qvarum ope tolli possunt  et n ex aequ 2
sed nos primum ope ipsarum 1 et 2. tollamus b. Ex aeg. 1. est b= cort
 quo  abstituto in aeq. a. fit c: 9+ co: fi n - nc: 14 + c0. p - n = p + p9
seu co - nco r9+ c: p - n (= p + p9(. 9 + co: p - n. jaml pue jan
jam pro n ponatur 1 - h ex aeg. 4 et pro 9 ponatur 1 - v. et pro
9+cop n 9- n ponetur (13 - 2Y v + v  1+ 24h- h Ae
5
per
pend
ex aequ et fit ex aeq.5 fiet. Co- neo pro 49. 5. scribatur per compendium
Cd2 = nco  = p + p9 (d seu neo C = p 12 p 9 + pas C - 2p 4+ 2pas co  + Co
seu V h +si. C0  Co: p 24. V V + ph- h seu 
seu co - V-ha C = p + p ep = pVO2. quod si rejiciamue omnia comparatione appositorum transcen–
dentia fieret O = - 2 v + 2h + Co: B2 imo fieret C = c. P  sed ita evemnescert
ne opus sit prolixo calculo, et ul
et is atet nec quiequam haberetur. Itaque