# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068207:0107
# Permalink to this reading: https://leibnizlegible.com/page/00068207:0107?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 54r, page id 00068207:0107
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 53v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=107
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000107.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 92 lines, status machine
# Lines: 92 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.

et 229C + - rul 42i lepp
u b rige 11 tir 1e9. E4
tiet -e ab facaoreb +44 ac -   ro
si Ax+ fad =  19. a fit an
ua
vv- ab +. Ja 
Gatac = orv. ab +G8 Hac
=aretaabharue
si desiderassemus
 X + mXX et X - mXX
esse quadratos, fuisset similiter
auan t at = grn M
2 tan ag tan
94- aa, Van
1e
vy - 4aa88a
gt+ at-racgss, an
qu (Cs + au)
apem= prgy _ et X= a
qusiversen X- a. votam
it foet vo-gy = 2am
aX + aux
nempe summum
me L ex else poratu
diferentiam ipscrum
fieretraam:, yy aa
r= aam:, vetaa
foret y = vB = 2aa
fierd potest yt D = 2B
et y y - v = aa: C
fieret 2y = 23 + (aa: β3)
et 2V = 2B- (aa: B)
yyt gy vv al
 at:, 23+ a qua  - a
   pera
Efficeere ut datus nunerus an sit differentia
ductum quadratorum se avu- vyanfiat
a y + b = β et y - v = an: β
ldux
Efficere ut datus numenis sit, dfsumma horum
ductum oc non ita facile est:
VY F vv = an
y + v -1 = β y - v1 - 1 = an: β
fieret, y = B + an: β
2v L-1 = B - an: B
Hica . et CXn. ), se Aones  intercurant
Jy an vo
si n esse b
imaginariae. Sed si volumus adhibere irra-
tionales, vel si an sit quadratus his non estr
gy = an = W, sit py = tan +  et ayotant
siet 82 + ad = 2dan e unde datur y,
et a san F av:  Gian-qv,: a
itaque in numers facile potest quadratus dividi
unde datur.
in duos quadratos.
yu + ex LH. = an fit 3y eo Frbb = an- bb
at2PC + ee + 4+ 245, s = an
dd si numerus datus semel dividi possit in
d duos quadratos, poterit infinitis modis
dioidi in duos quadratos verb. gr.
yy + vB = am sit. an = ee + A
fiat y -1Zae et v = tZaf, fiet
Y3 + vo = aa22 B2aa Ze F eP + 1FZ- 2laftZ + aaff - an
unde fit aZ Z = 2ft + 2ae,:, aa + Ht
yyton +2ry amt2ry
yy o - an 5NV
un numens an sit divisibilis per
vo eevo = an
er) vo
ponamus an in ec+i esse quadratum
nc si efficimus obtianimus quaesitum
an = (ee +) PY vel S+ rr.
dat Numtrum dividae in duos quadratos
  2d ac + un 17 + . an =0
ece rec= an
Z vy = an -v = an voee
sit an duplum quadrati, = 2ec
fit yy - ed = ee - vv, et res facile proredit
si an esset siplum quadrati, 3ee
fierer yy - ee ec vo te
yy an, si an extribus
compuaretur
quad jatas qau ecberet; sit en
B=8+F. exy- e+e, fieret
otasse res
vtieteet 9 28f 1ff -es CetHrgg,
fieret 1 p42 e + + 2F = g9
et na = pV + 20 + 29
se gescoco +29oC + G + 288 = gg -9
fiet  89-8-
siet 8cdco + 2coC +25 = g+G