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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 15
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29X6. 167.
Invenire Triangulum Rectangulum
in numeris cums area sit quaoratus
Aio id problema esse imporsibile.
inter varias demonstrandi rationes hanc reperi
rucherrimam, quiatmultas alias praeclaras proplositiones
aptissimam ducit
Prop. I. Si sint duo triangula similia, et latus
A’unius fit multiplicatione lateris homologi  alterus
per aliquem numerum, (qui dictu a Mono
etiam arca illius fiet ex area hujus per ejusdem
rngu quadratum multiplicata.
Nam areae triangulorum similium
sunt inter se ut quadrata homolo
ctorum laterum, adeoque si latus sit
multiplicatione lateris homologi
per aliquem numprum; fiet quadra
tum lateris multiplicatione quadraet
lateris homologi per quadratum ejus.
dem numeri. Ac proinde, idem
est in areis Triangulorum ipsorum
Prop. TI. Si area trianguli trectanguli primitiv
in numeris integris, quadratus esse non potest; etiam
derivativi in integris, imo et trianguli rectanguli
Cujuscunqu in numeris fractis area non potest
esse quadratus.
primo Nam d Triangulum primo
tivum et derivatinum sunt similia,
ergo per prop. 1. area primitivi fit
ex dinisa areadernitivi per quadratum
numeri derivativum metientis. Ergo
si area deliitivi est quadratus, etiam quod
ea per quadratum divisa fit, nempet
area primitivi erit quadratus. quod
si impossibile ostendatur etiam arsam
dervativi quadratum non esse posse
palet
Trianguli  rectanguli in
numeris rractis latera reducan
tur ad communem denominatorem
umat
decundo