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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 20
# Folio 11v, page id 00068269:0022
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068269&page=22
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aliquis
etiamsi unus ex continuis transsiliatur
s
lino loco continuorum substitui possunt
numeri progressionis arithmeticae, quicunque
et in universum alii quicunque, ubi impossi
bile est unum aliquem ex illis
caeteris singulis condivisibilem esse.
heorema illud a Freniclio 
peculiari libello demonstratum, quod scilicet
triangulum rectangulum in numeris, cujus
area sit quadratus, impossibile est
h ex huc nostri gener alissimi theorematis
Casu speciuli pendet. Nam  alibi
ostendimus trianguli rectanguli in numeri
latera circa rectum esse 2cd. cd =C
unde area trianguli: ed ed quae si
quadrato numero aequalis est, etiam divisa per
quadratum c. quoici dabit quotientem
d3- d quadralum; at quantitas da
d.d est productum ex tribus numeris continuis
seu sola unitate differentibus d-T. d. d+
anumerum ergo d d. impossibile est esse quadratum per
Theorema nostrum. Quare triangulum quoque
huigmodi in numeris integris dari non potest
cujus area sit quadratus. Quare nec in fractio
nam si fracti ad communem denominatorem
reducantur, et per eum mulit multiplicentur
provenient numenis in integris idem ha–
h praestantes
Caeterum  a3 d. aequ. fr. esse aequationem innumeris
imposibilem, amler etite seu a - d = f2 aequi0 non
posse produci ex aliqua td + nf + n t + pdn aliam
arbitririam od + rd +5F + t f2 + vds ex hoc calculo
generalissimo facile patet nullos licet adhibitis
theorematis nullam reblatione ad integros reductione facta