Full text: Volumen primum. Opera mechanica (1)

HOROLOG. OSCILLATOR. mam quadratorum à perpendicularibus, quæ ab univerſis
iiſdem particulis cadunt in rectam datam per E punctum.

104.1.

47. lib. 1.
Eucl.
Figure 1. Pag. 142.
TAB. XX.
Fig. 1.
D L F K A E G H C L K F D B
Figure 2. Fig. 2.
D F K L C H E G A K F L D B
Figure 3. Fig. 3.
L D C A E H G B L D
Figure 4. Fig. 4.
D L C E A X V G H L D B
Figure 5. Fig. 5.
T F K A V Q Z D E O B X P C Y f I G M L R N S H
Figure 6. Fig. 6.
K E A H C L D F G B
De centro
OSCILLA-
TIONIS .

Illa vero prior quadratorum ſumma colligetur hoc modo. Ponatur primò figuram planam dari O Q P, ad latus figu-
ræ ſolidæ A B C D, ejuſdem cum ipſa altitudinis, quæque
ſit ejuſmodi, ut ſecta lineis rectis Q Q, R R, quæ reſpon-
deant planis figuram ſolidam A B C D ſecantibus M M,
N N, & his parallelis; eadem ſit dictarum linearum inter
ſe, quæ & planorum horum ratio, ſi nempe ſumantur utrin-
que quæ in ordine ſibi reſpondent. Ut ſi linea R R ſit ad
Q Q quemadmodum planum N N ad M M. Quod ſi igitur
figura plana O Q P, in totidem particulas minimas æquales
diviſa intelligatur, quot intelliguntur in ſolido A B C D,
erunt etiam in unoquoque ſegmento figuræ planæ, velut
Q Q R R, tot numero particulæ, quot ſunt in figuræ ſoli-
dæ ſegmento M M N N, iſti ſegmento reſpondente; ac
proinde & ſumma quadratorum, à perpendicularibus o-
mnium particularum figuræ O Q P in planum E G, æqua-
bitur ſummæ quadratorum, à perpendicularibus omnium par-
ticularum figuræ ſolidæ, in idem planum E G productis. Il-
la autem quadratorum ſumma data erit, ſi dentur in figura
O Q P, cuneoque illius, quæ propoſ. 9. huj. requiri dixi-
mus. Ergo his datis, dabitur quoque ſumma quadratorum,
à perpendicularibus quæ, à particulis omnibus ſolidi A B C D,
ducuntur in planum E G.

Ponatur nunc alia item figura plana S Y T Z, cjuſdem cum
ſolido A B C D latitudinis, hoc eſt, quam includant plana B Y,
D Z ſolidum contingentia, ac parallela plano E A C, quæque
ſit ejuſmodi, ut, ſecta lineis rectis V V, X X & c. quæ reſpon-
deant planis figuram A B C D ſecantibus, K K, L L, & his
parallelis, faciat eandem inter ſe rationem linearum harum
atque illorum planorum, ſi ſumantur quæ ſibi mutuo reſpon-
dent. Itaque rurſus quadrata ſimul omnia perpendicularium,
à particulis figuræ S Y T Z in rectam S T cadentium,
æqualia erunt quadratis omnibus perpendicularium quæ, à
particulis ſolidi A B C D, ducuntur in planum A C. Illo-

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