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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 14
# Folio 107v, page id 00067976:0214
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Ex datis lateribus trianguli rectanguli
lateribus circa rectum hypotenusa sic per
Analysin Logisticam investigari potest
assumendo tantum illud principium vt
 quod triangulorum similium latera sant
proportionalia, quod  inteq primaria
habeo et in celculo inrspensabilate
Logistico indispensabiliter supponenda:
s angulus rectus Quemadmodum et quod tres anguli trianguli
sint onobus rectis aequale
BC
quaeritur longitudo ipsius AC. ut ergo verriamus ad calculum
ex B agatur normalis in Ad, habemus quatuor incognitas
AD, CB, AC, sed pro iis investigandis habemus et quatuo
tres aequationes nam ob triangula, similia ABC, ADB, BdC,
fiet AD: AB:: AB: AC seu AD = AB. AB: AC et CD. BC. CD est
a
CD: CB:: CB: AC seu CD = CB. CB: AC. jam
AD+ DC = AC. Ergo per  ex 3 per 1 et 2. fie
ABqu. + BC qu
: AC = AC turqu
enique ABqu + BC qui _=
AC qu Quod erat dom
AD. AC  ABqu similiter CD. AC= BC qu.
Ergo
AD+ X
AC  ABqu. + BCqu