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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 82r, page id 00068193:0165
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Sect. III. Cap. 2. De Potennia motrice absoluta.
Undo infra prop. 7. ostendemus, actiones etse in ratione compo-
sita temporum et potentiarum, seu ut rectangula sub tempo-
ribus et potentiis. Vistinguo autem potentiam mobilis abso–
c
lutam. in corpore per eo consideratam, a respectiva, qua ali-
ud percutit; de qua suo loco.
C
Rpop. 1.
Si duo mobilia eandem habeant materiae quantita
tem eandemque velocitatem, erunt potentiae iptorum aequalet.
Sint (Fig. 8.) mobilia aequalia A et B, et velocitates eo-
rum aequales; etjo et potentias eorum etse aequales. Nam ob
velocitates aequales continuato uniformitur motu aequali, ae–
quales describent longitudines (per defin. 2. C. 4 Sccr. 2.) Htaque
actiones erunt aequales (per. def. 3. C. 1. Sect. 3.) Ergo et potentia.
per defin praeced. hic).
Prop. 2.
Si duorum mobilium velocitates sint aequales, erunt
potentia eorum motrices absolutae in proportiono iptorum
mobilium.
sint. (3 jg. 9.) mobilium ABC (librarum duavum)
et LMND
librarum trium) velocitates aequales; Dico etu
potentiam iphus AB ad potentiam ipnus LM X ut mobilo
c
Ac ad mobile LMX (seuut 2 ad 3). Si AB et L M sint com
mensurabiles, sumatur eorum mensura communis f. Jam
cum quaelibet pars ipsius ABC vel LM NP aequalis ipsi i, velut
AS, vel LM, aequalis sit, et praeterea aequali moventur veloci-
tate (subintelligimus enum semper motum esee aquidietribu
tum ubi per prop. 6. c. 4. Sect. 2. Velocitates eorum, quae mobili ei-
dem insunt, sant aequales) erunt eorum potentia aequales sper
prop. 1. hic) verto gr. potentia ipsus AB aequalis est potentia
ipsius LM. Ergo totues aequalio potentia mert mobili cuique,
quotieo