322 Petri Callegari 



2ai. «in ( A_t-60») 



00 = 

 OA = 



i2 V 3 4- 2 a ft. sin ( ft — 60" ) 



Vs. ■/( a2 + ii_2 aicos,(A + 60»)) 

 posito AB=c, deducilur 



h'^ — 2 ab. cosk c'^—a^ 

 OA — 0C=: -7 _ 



Vid^ + b- —labcOsik + GO"))— S ' 



ex qua aequatioue theorema superius propositum evideoiissi- 

 nie palet. 



i3. Expressiones reclarum (Fig.4 Tab.XXV.2*)OA,OB,OC 

 in secundo paragrapho repertas ad qiiadralum evehamus. Ag- 

 gregatum quadralorum littera Q denoteiur, et ideo erii 



Q=:a2-4-i^-+-3x^ — 2axcoso — 2b x cos (k — o). 



E doclrina calculi differentialis de maximis, et minimis obti- 

 nebimus 



1 /^Q\ 

 -- 1 - — I = 3 X — a cos'o — bcos(k — o) = 0, 



1 ldQ\ 



(P) -(-— ^1 =(asmO — £.sIn(X — o))x = 0, 



2 \a of 



ex quibus aequationibus luculentissime sequentes deduci pos- 

 sunt 



(Q) x = — I ( a + i cos A) cos fi? -4- 6 sin O sin k\, 



( a -}- i cos ft ) sin o =: 6 sin ft. cos a. 



Ex hac postrema quadrando , atque 1 — sio^ co substituendo 

 pro coi>- 00, oblinebilur 



b sin ft 



sin O -zz ■ } rr -R — ; 7-: 



V ( a2 -I- t^ 4- 2 o ft cos ft )• 



Si bic valor in aequalionem cos' a* -t- sin* « = 1 infertur, erit 



a-\-b cos O 

 ~ V ( a' -f- ft- H- 2 a ft cos ft )' 



Ideo ( in aequalione (Q) positis valoribus sin &>, cos <« ) e- 

 licietur 



