Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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10667HOROLOG. OSCILLATOR. dem ſuperficiem vel aliam ſimilem ſimiliter que po-
11De de-
SCENSU
GRAVIUM. ſitam feratur, æqualibus temporibus per idem ſpa-
tium deſcendet atque aſcendet.

Velut ſi per ſuperficiem A B deſcendat mobile, atque, ubi
22TAB. VI.
Fig. 4. ad B pervenerit, converſo motu ſurſum per eandem A B, vel
ei ſimilem & reſpectu plani horizontalis ſimiliter poſitam
B C, aſcendat, conſtat ex ante demonſtratis, perventurum
ad eandem ex qua venit altitudinem. Cum autem perpetuo,
in punctis quorum eadem altitudo, eandem velocitatem ha-
beat aſcendendo ac deſcendendo ; apparet eandem 33Prop.
præced. bis eadem velocitate ſingulis ſui partibus percurri: unde &
tempora utriusque motus æqualia eſſe neceſſe eſt; quod erat
demonſtrandum.

PROPOSITIO XII.

ESto circulus A B C, diametro A C, cui ad an-
44TAB. VI.
Fig. 5. gulos rectos ſit F G; huic vero occurrat à ter-
mino diametri A educta A F extra circulum, quæ
quidem neceſſario ſecabit circumferentiam, puta
in B. Dico arcum B D, lineis G F, A F inter-
ceptum, minorem eſſe recta D F.

Jungatur enim B C, & ducatur ex B puncto tangens cir-
cumferentiam recta B E, quæ neceſſario occurret rectæ F G
inter F & D. Eſt igitur angulus B A C in circulo æqualis
angulo E B C . quare & angulus F B E, qui una 55Prop. 32.
Lib. 3. Eucl. E B C conſtituit angulum rectum F B C, erit æqualis B C A.
Quia autem ſimilia ſunt triangula A B C, A G F, erit &
angulus F æqualis angulo A C B. Ergo idem angulus F æ-
qualis angulo F B E. Itaque iſoſceles eſt triangulus F E B,
habens crura æqualia F E, E B. Addita ergo utrique eo-
rum recta E D, fiet F D, æqualis duabus B E, E D. Has-
ce vero duas majores eſſe conſtat arcu B D, iisdem

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Scan	Original
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