# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068124:0076
# Permalink to this reading: https://leibnizlegible.com/page/00068124:0076?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 38v, page id 00068124:0076
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=76
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000076.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 66 lines, status machine
# Lines: 66 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.

l+m aequ. abc (+ m- Im aequ. bC d. fiet: l’+m aequ a VC3
Pt mtum aqu. abC. Ergo 3Im aequ aeb   - bc 43g
Ero (aequ l+m aequ. O. Im aequ. D. fier laequ. O - m. aequ 2. Ergo 
m -Om  D. seu m - abCm + ~btC - b C d3 aequ. 0.
v
a
seu m - abc M + a bc aego 46b  1b4
+ bc d
ergo a- a b + bd deber esse quadratus.
2
l’anhago n = ph. lmago h  -p Ergo h. H - dm+ nm ago nn + np + pP
exaego 2 est HF lEago h. np = in. et llargo hhnn = 2tlinp +titi pp = Etrru t 2hipin + min
et lm aeqol hmn-lmp-mm. unde ex oqu 3. fit
hun -Erup + t p tk cum - tit mps hrum + h in) aeg nn + isut ps quam divellemus in mas:
htun -thmn aego nn et - 2khap t. tppo - tit mp aequ up + pp
hena-2henp + Lp-Onhu +  hm (htm (= th mod (AtM n  + L mm + Emm Eago nn + n p + pp
Mtstirmm
M
quodso ponatur haego 1. habebitur solutio, nempe valor ipsius n.
et eut naequ. P + 3pn +3Brum = P et laego P (3m (= 3um  PD - pp (3m p) im p-Bpun
3P + 3m seu lago. p - 2mp n-bum - appo
+3m
3p + 3m
Est te alias ob triangulum rectangulum, n aequ Z. quod nihil tabat,
jam
et leg  et p l. M. p sunt XX - y7 . 2xy. XX + y7
sit aego 2Xg. et B aego XX + yy et m aego XX - yy
fiet 2xy aequ Xxagy = 3x + 35 - 6x - 6f + 12 XXyy - 4 v  - 4y - 8 X y
6XX
V- WV+ L qu 2t 
seu 12Xy aego XX + gy - 13∞ - 7 yt + 4 Xxgy sit xaquy, fier 1   a y ay. 1357
sit Baego  ny fet 12 vhy aego Wyy 477 -13 v  - 77 +4 rvy et dividendo per gy
fiet irvius aequ v0 +1 - vgy - 7yt + vr gy
Ergo 3y + 10 _ aequ v0+ 1
v- voe
v= v+
rouv
Ergo v0 + 1, v- vv 1Z, +36V debet esse quadratus
seu C 37 vE (+V -vV +7 seu 37v + 5vv +7 debet esse quadratus.
4 +0d cujus resolutione habetur oblema
Resumamus calculam Marginalem paginae praercedentis quia ad exitum perduxisse visus est
vn
EL X =y + BI Exy + B) pxyy aequ Z3. fiet (a reyosuay y+ ou myse qu Z
y +  AX + 2. 8 3. 3y + X gy aqu. 6Z XX - 12XB + X y7.
364
Z  2X  + 1 XY 3Z 6X + BX
sxx
1BXX
36X4
seu 33+ ng aqu 16Z - 12X + X yy. Ergo 6Z - 1 X + X yy) aququadrato (+ 3y) + XyB + vo
6 X
et fiet. y lequ 62 - 12∞6- vr
2XXV
(91
et ex ago 5. 3yt 27) aqu (xry) + v. Ego fet: 62- 12X - rv aquS
ox
et fiet: Z aequi op2
e 6X
exo
(10)
fiat v aequ 6p49.
aequ 4. Et ex aequ. 9 habebimus: 62- 12 p r =- 36 pp aequ.   Y 4q
t prr aeio. b et p9qe aequ c fiet: pprigs q  u bct seu prosaego be   o ceper 14 et 15.
et ex aequ. 13. fier 673 - 12 b - 36 e aequ  b c Ergo 6 bc +  b + Ct debet esse cabus
quae quidem foret solutio generalis, nam inhildum assumsiuus pro arbitioo
et X aquprr