# Full text: Volumen primum. Opera mechanica (1)

HOROLOG. OSCILLATOR. datorum punctorum multitudinem exprimens, dicatur θ; erit
E R = {ι/θ}; & R G = {μ/θ}. Cumque G S ſit x, erit R S ſive
F T = x - {μ/θ}; vel {μ/θ} - x, ſi G R major quam G S; & ſem-
per quadratum F T = xx - 2 {xμ/θ} + {μμ/θθ}. quo ablato ab qua-
drato F E = zz, relinquetur quadratum T E = zz - xx
+ 2 {xμ/θ} - {μμ/θθ}. Et proinde T E = zz - xx + 2 {xμ/θ} - {μμ/θθ} . Erat autem E R = {ι/θ}. Itaque T R = {ι/θ} + vel - zz - xx
+ 2 {xμ/θ} - {μμ/θθ}
. quæ T R, brevitatis gratia, dicatury y. Colli-
gamus jam porro ſummam quadratorum omnium F A, F B,
F C, F D. Quadratum A F æquatur quadratis A V, V F. Eſt autem A V æqualis differentiæ duarum V K, A K, ſi-
ve duarum S G, A K; ac proinde A V = x - e vel e - x; & qu. A V = xx - 2 ex + ee. V F vero æqualis eſt differen-
tiæ duarum F S, V S ſive duarum F S, A L; ac proinde
V F = y - a vel a - y; & qu. V F = yy - 2 ay + aa. Ad-
ditisque quadratis A V, V F, fit quadratum F A = xx - 2 ex
+ ee + yy - 2 ay + aa. Eodemque modo invenientur qua-
drata reliquarum F B, F C, F D; atque omnia ordine diſ-
poſita erunt hæc; qu. F A = xx - 2 ex + ee + yy - 2 ay + aa. qu. F B = xx - 2 fx + ff + yy - 2 by + bb. qu. F C = xx - 2 gx + gg + yy - 2 cy + cc. qu. F D = xx - 2 hx + hh + yy - 2 dy + dd.

### 102.1.

Prop. 2.
huj.
Prop. 2.
huj.
De centro
OSCILLA-
TIONIS .

Horum vero ſumma; ſi ponamus quadrata ee + ff + gg
+ hh = nn; & quadrata aa + bb, + cc + dd = kk; erit iſta, θ x x - 2 mx + nn + θ yy - 2 ly + kk. Siquidem
θ erat numerus datorum punctorum ideoque & quadratorum,
poſitumque fuerat e + f + g + h = m, & a + b + c + d = l.

In iſta vero ſumma, ſi in terminis θ y y & 2 l y, pro y,
ponatur id cujus loco poſitum erat, nempe {ι/θ} + vel -
zz - xx + 2 {xμ/θ} - {μμ/θθ}
fiet + θ y y = {ιι/θ} + 2 l zz - xx + 2 {xμ/θ} - {μμ/θθ} + θ zz - θ xx
+ 2 x m-{μμ/θ}.

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