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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 15r, page id 00068195:0029
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res Numeri qui sint
Summa duorum torum
Differentia eorundem
Duplum Rectangulum
sub Lateribus
untra
Bas in vel Cathetum) verbo
latu circa
primitivi
Cathetum vel Basin) rectum) Cujuscumue
Triangulum rectangulum Numericum voco, cujus ni tria latera
omnia in numeris integris exprimi possunt. Latera, inquam, id est
hypotenusa sive subtendens angulum rectum; et et duo latera irca rectum, quorum
l alterutrum basis, alterum cathetus vocatur
Triangulum rectangulum Numericum primitivum est, cujus latera non habent mensuram communem
Theorema Monadicum
Solus. Numerorum (: untate najium) Binarius latus Frianguli Rectanguli
Numerici esse non potest: cateri omnes possunt.
d est quonium quadati sunt pur
uinet
 es
dasunt
divisa per maximam quam
habent communem ineu
Micmgut.
potenusam
rectanguli
Numerici
AC, 1. CbX. BE, y. yy aequ. 1 = xX seu y aequ. si -xx
hyaequ. a aquta ix aqtx, itia, i-Xx aequ. 1+X, 1+ x1+ YX, 1-1x. et
ila porro. 
posito Z esse inffinitur
=finitum hoc modo: yy aequ . - XX aequ. 1+ X, 1+ YX, 1+ VX, 1+, 1+X, et. 1S- S
Est autem 1 -  x aqu 1 - (Z) X Ergo si Z infinita fit = aequ. 0.
c
inde
sieb: IZ(x aequ. Fo(X aequ. 1. Ergo = YX aequ. 1 - 1 aequ. 0.  non quod omnino sit 0 sed quod
sit quantitas in finitesina ergo _2 lg aequ. 1 x + 11t ed  + Cit s 8c