268

CAPUT X. DE VARIATIONE

cc cofy (aa (aa — cc) cofa 2 -f bb (bb — cc) coff 2 )

tangCOS — --7- ; ---- : --

{aa — bb )cola coi Q(aabb — (aa —cc) (bb — cc) coi7*)

unde concluditur

dudlo autem arcu AO erit tangAOC =

cofa cofy

tang AOS —

aa cof« (bb {bb _ aa) cof£ 2 + cc (cc — aa) cofy 2 )

(bb—cc) coff cofy ((bb — aa) (cc _ aa) cofa 2 — bbcc)

C 0 R O L L, 3 .

672. Haec formula pro angulo AOS analoga efl illi pro anguloCOS, indeque oritur, fi litterae a, b, c, item a, £, 7 in ordine unoloco promoveantur: hoc autem modo fignum prodiret negativum, idquod rei naturae eft consentaneum, cum angulus AOS in fenfum contra-rium cadat refpedlu prioris.

C O R O L L. 4 .

673. Si arcus OS quadrantem AC fecet in pundlo R colligitur:

aa cofa (bb (aa _ bb) cof£ 2 + ce (aa - rr) cof<v 2 )tangAR — —-—- v ' 1 '

cc cofy (aa (aa — cc) cofa 2 + bb (bb — cc ) cof£ 2 )ac fi idem arcus 80 producfhis occurrat quadranti BA in Q erit peranalogiam:

bb cof£ (cc(bb — cc) cofy 2 -f" aa(bb — aa) cofa 2 )aa cofa (bb (bb —aa) cof£ 2 -f -cc(cc— aa) cofy 2 )

= cot AQ,.

C O R O L L. $,

674. Cum tempufculo dt arcus CO — 7 minuatur particula Op,erit per differentialia

a a bb cc dy finy = (bb — aa) dt cofa cof£(an bb — (aa — cc)

(bb — cc) co(y z )hineque per analogiam :

aa bb cc dk (m£ = a (aa — cc) dt cofy cofa (aa cc — (cc — bb)(aa — bb) cof£ 2 )

aa bb cc dx fot = « (cc _ bb) dt cof£cofy (bbcc — (bb — aa)(cc — a a) cofa 2 ).

SCHOLION.

€75. Aflumfimns in folutione, quod probe efi notandum, corpus<irca axem IO in fenfum ABC gyrari, ad quem ergo cafum formulae

inveii-