Full text: Bošković, Ruđer Josip: Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium

110. Porro poſito radio = 1, eſt ex Theoremate trium maſ-
ſarum ut P x P Q x 1 ad A x A Q x ſin Q A a, ſive ut P x
P Q ad A x Q a, ita actio in A perpendicularis ad P Q =
{P a/P Q} x V ad actionem in P ſecundum eandem directionem,
quæ evadit {A x Q a x P a/P x P Q 2 } x V: nimirum ob Q a = P Q -
P a, erit actio in P = {A x P Q x P a - A x P a 2 /P x P Q 2 } x V. Cum
harum ſumma debeat æquari zero demptis communibus {V/P x P Q 2 },
æquabuntur poſitiva negativis, nimirum poſita ſ pro characteri-
ſtica ſummæ, habebitur ſ. A x P Q x P a = ſ. A x P a 2 , ſi-
ve P Q = {ſ. A x P a 2 /ſ. A x P a}, vel ob ſ. A x P a = M x P G, poſito
ut prius M pro ſumma maſſarum, fiet P Q = {ſ. A x P a 2 /M x P G}, qui
valor datur ob datas omnes maſſas A, datas omnes rectas P a,
datam P G. Q. E. F.

30.1.

Calculus, &
formula deri-
vata.

111. Corollarium I. Quoniam a P æquatur diſtantiæ perpendi-
culari A a plano tranſeunte per P perpendiculari ad rectam
P G, habebitur hujuſmodi Theorema. Diſtantia centri percuſſio-
nis ab axe rotationis in recta ipſi axi perpendiculari tranſeunte per
centrum gravitatis babebitur, ducendo ſingulas maſſas in quadrata
ſuarum diſtantiarum perpendicularium a plano perpendiculari eidem
rectœ tranſeunte per axem ipſum rotationis, ac dividendo ſummam
omnium ejuſmodi productorum per factum ex ſumma maſſarum in
diſtantiam perpendicularem centri gravitatis communis ab eodem
plano.

30.1.

Theorema eru-
tum ex formu-
la.
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