# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0075
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0075?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 37r, page id 00068200:0075
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=75
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000075.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
# Lines: 55 recognised, mean confidence 0.87
# 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.

Area trianguli rectanguli in numeris
non potest esse quadratus.
post varias demonstratdi rationes hanc
reperi aptissimam
prop. 2. Si area trianguli non potest esse quadratus
in numeris integris, nec poterit esse in fractu
sit) latera trianguli rectanguli rectanguli in
numeris generaliter concepta sunt: circa rectum
Xv. 2XY. (quidem  X2-y et 227. a hypotenu sa X+y.
non es quad ra ergo area erit Xy - X93. (4) quodsi ergo X vel
dun
y vel uterque sunt fracti reducantur ad communem
nomnatorao. (5) Et fiet pro X, fiet  E: pro Y, fiat
co
(6) Et area erit FIV - x0 quae si quadrato
a
c04
aequatur ex hypothesiptiam multiplicando per quadr
4
tum co productum vo = E~E quadrato multi
u
rum differen plicabitur. (8) Est autem hoc productum area
trianguli rectanguli iun numeris cujus latera crca
rectum sunt ∞2 -V et 2EV., et quidem in inter
est quadmus pr 5 quia 8. v. sunt sintregrisper 5). Ut egu
Ergo dato triangulo quale quaeritur in fractis
dabitur et in intequis
E.
ro) Si area trianculi xaciusdam in numeris
earis primiivi nenots esse quadratur
jam artatriantum lijiscunq derinatiur
quadratus assa tian poteti
Demontntur eo tendem ubden Triangulum primi
quumest cum uia salone  suns primi interse
Verivatirum cum tro eutehatane doam pmoram
(2) egutduhite rectm Euudfactus ex later
bus cirra rectum, sea appa deplicuta
prop. TI. d omnis trianguli rectanguli in nume
ris integris derivativo area, dividi potest:
per quadratum, et si dinisor sit trianguli
laterum mensurae communis mercura sit ex quadrato
maximamensurae communis ducto in area in trianguli
e
sui pornilii alterius
patet ex generali Triangulorum doctrina, nam
areae sunt inter se in exposita laterum ratio
duplicata
homologorum
per integros
exprimendo
quadrutom
quotum
tia estqam
diatus ectum
sumima non