4 io CAPUT XVIII. DE MOTU CORPORUM

quantitates K et L funt ex natura corporis datae. Cum igitur hinc inven»tus fit valor iplius u, inde habemus j 1 = zfgi f, et

6 cof<? G cof»/ G cofS’

A =-—; R =-- ; C — --

i — aau i — bbu - i _ ccu

Gu (bb — cc) cofq cof!) G» (« _ coD^coC^

Q i — bbu)(i — ccu) ’ ^ (i - ccn) (i — aau)

Gu (na — bb) cof£ cof»)

Ct ^ ~ F(i —anu) (I - bbu)

Si jam initio fuerit arcus ZD — r, qui nunc eR q, cum fit initio p — D tE i r=F, habebimus

DD + EE 4- FF = rr,

unde per r invenitur confians G. Denique pro angulo A inveniendo— dt (B cof»; + C cofA) finjV

prodit A - --, ideoque A =

(B cofq + C cofZ) (cofjt -i)

--r—;—-- ii quidem arcus ZA initio tuent in verti»

califixo, indeque in fenfum XOY moveri fumatur, quatenus ergo haecexpreffio pro A efi negativa, in lenium contrarium axis IA circa 'L gyrarieft cenfendus.

Denique cum fit/?/? ■{■ qq rr = qq, erit q = r cof< 5 it, ob r = /"(DD + EF 2 + FF), unde patet axem ID in filum verticalem erigi elapio

tempore = —et titubationes ifochronas fore ofcillationibus penduli,

. . , „ 2 g 1 K-/(KK_ 4 L)

cujus longitudo eft = —rr- — — — -—-.

M fu aL/

COROLL. u

904. Cum fit DD + EE + FF = rr, erit

< 5 'thr = AA (cof», 2 + C(>f 3 *) + BB l cof^* + cof 1 &») + CC(cof^*4 - eof»j 2 ) —aKt' cofycofA- aACcof^cofi}— aABcof^cofjjet quia G — A cof£ 4. R cof»; 4 - C cof A, hujus quadratum eo additum dabit$hv + GG= AAf RR + CC,

ubi fi brevitatis gratia ponatur --— — P; - - — = 0 ; —--

1 — aau 1 — bbu 1 — ccu

— R, ob P cof£ 2 4- 0 cof»j 2 4- 0 t cof A 2

1 et A = GP cof£ R —