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

336. Deinde debet centrum gravitatis jacere inter punctum ſuſ-
penſionis, & centrum oſcillationis. Sint enim in fig. 64 pun-
cta A, P, G, Q eadem, ac in fig. 63, ducanturque AG,
AQ, & A a perpendicularis ad PQ; ſumma autem omnium
maſſarum ductarum in ſuas diſtanti
as a recta quapiam, vel
plano, vel in earum quadrata, deſignetur præfixa litera ſ ſoli
termino pertinente ad maſſam A, ut contractiores evadant de-
monſtrationes. Erit ex formula inventa PQ = {ſ. AxAP 2 /MxGP} Por-
ro eſt AG 2 = AP 2 + GP 2 -2GPx P a, adeoque AP 2 =
AG 2 -GP 2 + 2GPxPa, & ſ. AxGP 2 eſt MxGP 2 ,
ob GP conſtantem; ac ſ. AxPa eſt = MxGP, cum P a
ſit æqualis diſtantiæ maſſæ a plano perpendiculari rectæ QP
tranſeunte per P, & eorum productorum ſumma æquetur
diſtantiæ centri gravitatis ductæ in ſummam maſſarum; adeo-
que ſ. Ax2GPxPa erit =2MxGP 2 . Quare {ſ. AxAP 2 /MxGP}
erit = {ſ. AxAG 2 -MxGP 2 + 2MxGP 2 /MxGP} = {ſ. AxAG 2 /MxGP}
+ GP. Erit igitur PQ major, quam PG, exceſſu GQ =
{ſ. AxAG 2 /MxGP}.

22.1.

Centrum gr [...] -
vitatis debere
eſſe inter bina
reliqua ex iis
punctis.
Fig. 64.

337. Ex illo exceſſu facile conſtat, mutato utcunque puncto
ſuſpenſionis, rectangulum ſub binis diſtantiis centri gravitatis
ab ipſo, & a centro oſcillationis fore conſtans. Cum enim ſit
QG = {ſ. AxAG 2 /MxGP}, erit GQxGP = {ſ. AxAG 2 /M}, quod pro-
ductum eſt conſtans, & habetur hujuſmodi elegans theorema: ſingulæ maſſæ ducantur in quadrata ſuarum diſtantiarum a cen-
tro gravitatis communi, & dividatur omnium ejuſmodi produ-
ctorum ſumma per ſummam maſſarum, ac habebitur productum
ſub binis diſtantiis centri gravitatis a centro ſuſpenſionis, & a
centro oſcillationis.

22.1.

Valor conſtans
producti ex bi-
nis diſtantiis
centri gravita-
tis ab iiſdem.
Manente pun-
cto ſuſpenſionis
& centro gra-
vitatis, manere
centrum oſcil-
lationis.

338. Inde autem primo eruitur illud: manente puncto ſuſpen-
ſionis, & centro gravitatis, debere etiam centrum oſcillationis
manere nibil mutatum; utcunque totum ſyſtema, ſervata reſpe-
ctiva omnium maſſarum; diſtantia, & poſitione ad ſe invicem con-
vertatur intra idem planum circa ipſum gravitatis centrum; nam
illa GP inventa eo pacto pendet tantummodo a diſtantiis,
quas ſingulæ maſſæ habent a centro gravitatis.

339. Sed & illud ſponte conſequitur: centrum oſcillationis, & centrum ſuſpenſionis reciprocari ita, ut, ſi fiat ſuſpenſio per id
punctum, quod fuerat centrum oſcillationis; evadat oſcillationis

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