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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 164r, page id 00068193:0333
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Sect. WV. De Causa et Effertu activis.
3(4) potentiae elevandi sunt aequ’ales.
Nam causae plenae sunt effectitus integris proportionales
C
(per prop. 11. huc); Cum ergo pondera ad altitudines ipsis reu-
a
proce proportionales elevata aequalem potentiam habeant (per
prop. 15.) eunt et potentrae elevandi in causis elevare valen
tibus aequales.
Dubitari sclicet, poterat, annon elevandi idem pondus ad
es
candem altitudinum diversa sit potentia pro diversis elevandi
modis, ita ut diversa ratione elevandi eadem potentia possit
idem pondus elevare plus vel minus. Sed constituto semel auio-
 mate, quod usa plina effectui integro aequivalet, eadem sem
ris per potentia ad eundim effectum determinatum potentia
prad
itum quomodocunq producendum requiretur.
Top. 18.
on libra reetilinea si distantiae ponderum a centro
horationis sint ponderibus proportionales reuproce, tunc
s
ret aequilibrium.
Smt (fig. 8.) pondera A et B, quae librae rectilinea
ACB extrema puneta sA, 1B, tota sua vi trahere conen
tur versus horinontim HR. sitque C uA ad C1B, ut pondus
B ad pondus A; vertigr. si A pondus sit duplum ponderis
B, sit distantia a C centro librationis, nempe BC, dupla di
stantiae AC; Duco pondera esse in aequilibrio. Ponatur enim
elevari alterutrum ut A, ex 1A in. 2 A translato 1d im 2B,
et
libra 1AC, B translata in 2 AC= B, situm verticalem; du-
cantur perpendiculares ad verticalem, 1AD et 1BE; ob trian-
gula CDiA et CE1B similia, erit CD ad Cst seu ad C2A, ut
et
rum
e ad
e port
inet,
equ
Anor
Aiad
atart
ad 2
M4
entr
em
C nunu
ales
eleva
evate
 
es se
altr
eribuo
hobet