# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068160:0009
# Permalink to this reading: https://leibnizlegible.com/page/00068160:0009?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 5r, page id 00068160:0009
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 4v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068160&page=9
# Source image: https://digitale-sammlungen.gwlb.de/content/00068160/jpgs/default/00000009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.77
# 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.

vens ha e= p: 4 = aY. et 27 - = s Se- p. 2
344+5 =125e. 2=6)
3+ 4 -5 = 2; : 2 = 1 (136
3-4+5= 43
= 2 =
2
3+4+5= 6; : 2 = 3
et FM = hSe -p: 2Y.  C et  sit FGseu q. Y = n. fiet: GM = Inn -F p
seu = S  99 447+- h C21 kp Sarrnn- hhee +hhpp : 2Y
jam GD: DL:: MG+GF. H MG et GD = ad : r. fiet DL = MG. aB: Y AnGF GF
Triang.
seu DL = MG. ab: Y MG+ n multiplicetur per GLe tam num erator quam
nominator per MG+n. fet DL = MG. ad. Y MG   ad-MG 4 n MG: r. MG = tin
jam MG + nn = FM et fiet DI = 4Y aD FM= nN +n MG: hi  et p
jam seu D1 = ad ln ee pp erena tarrumque. rte cp vel si MG
vocemus m. fiet: DL FM vocemus m, fiet et MG, g. fiet: DL = ab po-g
d
jam alibi invenimus esse DL = ad Seepp - ggrr: hrp ergo scribendo eepp. qur-H
aao
fiet DL = ab T: hrp. et duos valores aequeendo fiet ng gg: mn .: L. hp 
vel nghp-gyhp= umtt. debent autem aHolli ad quadratum et L
ad quadrato quadratum, ut totlatur irrationalitas, et fiet:
nnpp= m (E+ mmtt ggtip + g thpp. Et rursus compendii causa
runsus scribatur nt compendii causa mee pp- ggrr: hp vocetur f
et fiet ng-g9 = t debet  ita attolli ut 4 assurgat  ad quadratum, et f
ad quadrato quadratum, tg fiet ng = t + gr. seu ng = V + 169+
6.
4
eda
est1aa
c
rursus nngg -  - st = 2 tg. et fiet (4 g = n g - 2nnggt 2 nng+ l( 2tg14
al
2V4
seu 2Fg+  2n g t +2 = ntq + ++ g
C2
est n seu 2 i cerp qqrr. lip. arrun-hhee +. hhpp: 167)
a
a
r t ceti 
2n. 4Yn - E C +h p: 4Y. m ep - qr. ti p 
n arru ee +hhpp: 167+
P = r- n su N = r- p
X +ist = V. X = v - Y, v+ y = 2m V- y = 2ln fiet X = dnn
nam v- tm + lm,: 2 et y - lm - tm :2. sit l= 2 et m= 1
fiet  2 et v = 4 et y et v = lm + In et y -lm - ln:ll
sit  l= 1 m = 2. n = 1 fiet v = 45 et y = 3 et X = 4
sit l= 2 m = 2 n = 1 fiet : v = 10 y = 6, et x = 8. itaque si caeleris
manentibus variatur l, manent triangulum rectangulum idem specie lant
Ergo semper ponamus l = 1. et nunc sit m = 3 et n = 1 fiet,
a V = 10 y = 8  X = 6 nam 15 +36 quod rugus simile priori
sed si sit l =01 m = 3 n = 2. fiet y =5 x = 12 v = 13
23