Full text: Volumen primum. Opera mechanica (1)

HOROLOG. OSCILLATOR. quæ velut luxatione illarum efficiuntur, ut trianguli ſcaleni,
& parabolæ non rectæ, centra oſcillationis haberi. Ut ſi,
exempli gratia, triangulum B A C iſoſceles, cujus axis
A D, à puncto E ſuſpenſum intelligatur; ſit vero & aliud
triangulum ſcalenum F A G, axem eundem habens A D, & baſin F G æqualem baſi B C; etiam hoc triangulum, ex E
ſuſpenſum, priori B A C iſochronum eſſe dico.

120.1.

Figure 1. Pag. 164.
Fig. 1.
G B O N C R P F
Figure 2. Fig. 2.
G B R F
Figure 3. Fig. 3.
A E C F B
Figure 4. Fig. 4.
A C E D F B
Figure 5. Fig. 6.
A B C G D L
Figure 6. Fig. 5.
H A O M R L N
De centro
OSCILLA-
TIONIS .
TAB.XXVII.
Fig. 1.

Quia enim virga, ſeu linea gravis, F G, affixa virgæ ſi-
ne pondere E D in D, ſitu obliquo, ſuſpenſaque ex E,
iſochrona eſt virgæ B C, ſimiliter in D affixæ ; idemque evenit in virgis cæteris trianguli útriusque, quæ axem A D
ſecant in iisdem punctis, atque inter ſe æquales ſunt: ne-
ceſſe eſt tota triangula, quæ ex lineis, ſeu virgis iisdem
compoſita intelligi poſſunt, iſochrona eſſe. In aliis figuris ſi-
milis eſt demonſtratio.

120.1.

Prop. 16.
huj.

121. PROPOSITIO XXII.

QUomodo, in ſolidis figuris, oſcillationis centra
inveniantur.

In ſolidis porro figuris facile quoque, per ante demon-
ſtrata, centrum oſcillationis invenire licebit. Si enim ſit ſc-
lidum A B C, ſuſpenſum ab axe, qui, per punctum E,
intelligitur hujus paginæ plano ad rectos angulos; centrum
autem gravitatis ſit F: ductis jam per F planis E F D, G F H,
quorum poſterius ſit horizonti parallelum, alterum vero per
axem E transeat; inventisque, per propoſitionem 14, ſum-
mis quadratorum à diſtantiis particularum ſolidi A B C à
plano G F H, itemque à plano E F D; hoc eſt, inven-
tis rectangulis utrisque, quæ, multiplicia ſecundum numc-
rum dictarum particularum, æqualia ſint dictis quadratcrum
ſummis; rectangula hæc applicata ad diſtantiam E F, qua
nempe axis ſuſpenſionis diſtat à centro gravitatis, dabunt
intervallum F K, quo centrum agitationis K inferius eſt
centro gravitatis F. Hoc enim patet ex propoſitione 18. Da-
bimus autem & horum exempla aliquot.

121.1.

TAB. XXV.
Fig. 5.

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