BASI SPHAERICA PRAEDITOR. SUPER &c. 425

C O R o L L.

933, In genere autem quicunque motus corpori initio fuerit impref-

. , et (aa cofa cof? — tc cofb fin?)

fus, erit XZA = a = 180° - (-*-- y-j- -—

cici cof? + cc fin? 2

licqitc arcus ZA uniformiter circa pundtum verticale Z circumferetur: de-inde vero cum fit fm AD : fin DZA = ZD (e) : ZAD, erit ZAD —r fin l cof(<^ + f>) „ r cof l cof(< 5 V + g)

- atque arcus ZA = ? — —-

fin £ coi hpro g et h fubllituendis valoribus:

r fin l cof$'t

angulus ZAD — ---—-- -

tt arcus ZA = ? — V cof l cofjY -f-

Seu

cofg

e (cofa fin? 4 cofb cof?) fin

k cofe fin Ft

i-ihi

S C H O L I O N.

924« Hae tres pofiremae formulae, angulos X?,A, ZAD cum arcuZA exhibentes, totam problematis folutionem complechmtur. Quodfienim has res ad quodvis tempus afiignare poffimus, litum corporis per-fedle cognofcimus. Quare fi pro F et valores fu pia inventos fubilitua-nius, univerfa problematis folutio his formulis continebitur:

et (aa cofa cof? — cc cofb fin?)ang. XZA= 180 0 — i -

fin

H *fg

aa cof? 2 4. C c fin ?

, tJifg ec cofe

r>rc. ZA = ?-- r cof f coi - + — - — —

b c /2/§

r fin l t-fifa {aacol? 2 4 cc fin? 2 )

ang. ZAD = — y-j— cof —-— - t-JL -k_L

Jm? ac

eae (cofa fin ? 4 cofb cof?) ^ t/ zfgjaa co f? 2 4 cc fin? 2 )

fin i/ifg (aa cof? 2 + cc fin ? 2 ) _ ac

Quodfi ergo omnia momenta inertiae fuerint aequalia, fcilicet aa = ff,erit ang. XZA — 1 go° — i - et (cofa cof?— cofb fin?)

arc.Z A — ?— x cof l cof

tfzfg

4

;C cofe

fin

t/*fg

rfinl r t/2fgang. ZAD — ——- cof ——_fin? c

quo cafu pofitio puntffi A efi plane arbitraria,

Hhh

/ *fg

f r(cofo fin ?4 cofb cof?) tyfifg~~ Cm (/ 2 /g m ~ C

SCHO-