446 CAPUT XIX .DE MOTU CORPORUM ta.

C — 4 fg coff —ffrr fin ^ 4 — F»'»' + iru (D cof^ + E fin^») 4 " I(S(A coi £ 2 + 1^3 (iiif coff + d fin^ 2 ) ex quibus concluditurDD — ('# cof^* 4 - 2 B fin^ cof^ + (£ fia£ 2 )(C_ 4 fg coff)

(D cof§> 4 -E fin^) 2 —(Acol^> 4 4° 2 E fin^>cof^>4-C fiu^ 2 )^F4-^"fm^ 4 )Hinc pro tempore adipifcinuir t‘=z f ————

vr

D — r (D coff + E fin f)

erit angulus (p = _ fudt = f

et cum fu « =ud{>

A cof^ 2 4- 2B fmf cofg 4 - @ l' n f 1 ,

Cum autem ad quodvis tempus t tam arcum 'q quam angulum <p determi-naverimus, totus motus erit perfcde cognitus.

C 0 R 0 L L. I.

952, Quantitates ergo %, C, et F neceffario funt pofitivae, et Bad A et V ad A et C ita refertur, ut Iit

AC — BB — aabb fin (j* fin A 4 4- aacc fini) 2 fim? 2 4- hbcc finf 2 fin^ 4unde patet, formam A cof§> 2 4- 2B fin§> cof§> 4- C fin^> 4 in duos fadloresfimplices refolvi non poiTe.

C O R O L L. 2.

953. Ex hac folutione generali cafus in praecedente problemate evo-lutus facile deducitur, fumendo f negative, et arcum infinite parvum,DD - ?(C _ 4^J ^ g cof^ _ Cond. 4- 471 /g coff

- - A/-DD '

unde fit rr =

DD-AF

Reperitur autem valoribus evolutis

AF — DD = aabh coft ) 2 fin A 2 4- aacc cofg 2 fin*/ 2 4. hbcc colf 2 fin £ 4

unde longitudo penduli fimplicis ifochroni fimplicius quam ftipra ita exhi-

aabb coft ) 2 fm$* 4 - aacc cofq 2 lina 2 + bbcccofi 2 fin ? 4ut Iit = ------ N

betur,

f K aa col^ + bb coC ?; 2 + cc cof& 2 )

S C H O L I O N.

954. His de motu corporum cylindricorum fu per plano horizontaliexpeditis, infiitueram pauca de motu fuper plano inclinato adjungere: ve-rum fi motus fuerit fimplcx, res nullam habet difficultatem, fin autemfit complicatus, in calculos incommodos incideremus. Quare cum inpraxi fricffionem ab his motibus fc para re haud liceat, motus fi, Item fim-pliciores fuper plano inclinato ita pertractabimus, ut fimul fridionis ratio-nem habeamus, ex quo peculiarem traifiatum de motu corporum rigido-rum a fridtione perturbato adjungi conveniet.

ADDI-