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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 180r, page id 00068196:0355
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# Lines: 37 recognised, mean confidence 0.96
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quot
libratum sit
Si mobile A impellatur simul conatibus
14
AC, Ad, seu ita ab illis impellatur
perA
ut sit in aequilibrio, ducatur Ju recta
indefinita quaecunque LM, in quam ex
linearum virtute conatus repraesentan
tium extremis demittantur perpendiculares
BE, CF, DG abscindentes a recta in defnita
portiones AE, AF, AG, eRAF erit summa abscissarum
ab una parte aequalis summae abscissarum ab altera parte
et hoc loco quidem AE+ AF aequ. AG) si ab alterutra
parte esset excessus, in eam partem tenderet mobile
ipsa de differentia summarum. Haec est propositio
Johannis Cevae Mediolanensis in opusculorum mathema
ticorum parte 1. de potentiis obliquis. patet autem
vel ex eo (communi consideratione) quia conatus in AB
relatus ad lineam LM, est quasi conatus in AE, et ita
de caeteris. Nam ab ipso
Hinc ego infero consequen
tiam tatem, si mobile punctum A, ponatur impelli infinitis
virtutibus in omnes partes infinitis virtutibus simul, quae
repraesententur per curvam  ducaturque per Altanquam
centrum tadias in se redeuntis H H radios ex AH ex centro
A ad curvam ductos. ducaturque NP perpendicularis ad LM in A
patet Hg perpendiculares ex cuivae puncto H in Np demissas esse
abscissis (per perpendiculares ex H in LM demissis aequales, et
proinde um cum Hq sint ipsius curvae HH ordinatae ad XP, debet
hinc si summa ordinatarum, seu area curva ab una parte ipsius LM
rectam
major sit quam ab alia parte in eam partem feretur mobile
S aequalet sint erit in aequilibrio. Quod si secundum omnem
lineam in locu ipsius LM ductam mobile in aequilibrio est
necesse est curvam AH HH esse amphidextiam ila enim semper in
artes aequales figura secatur