256 
DISQUISITIONES GENERALES 
expressionis r sin cp. /cos cp'— r cos cp. /sin cp', quae fit — h c sin A, suppeditat for 
mulam sequentem 
cos A*cos A ■— — to — 0>sin^ji/°+i/> + i/(0-|-0') 
+ (tV/”— tV/°/°) PP + To9P [ < l~\~ ( i) 
+ (i^° — tV/°/°)(?? + ??'+?Y)+ etc.} 
Hinc fit porro, usque ad quantitates quinti ordinis 
+1hgp [q-\-q) J r\h Q [qq-\-qq-\ r qq ) 
—sV/°/° (7pp + 7 22+ 127 ?Y)! 
Combinando hanc formulam cum hac 
2o = ap{\ — if{pp-\-qq + qq + qq— etc.)) 
atque cum valoribus quantitatum a, 4 y in art, praec. allatis, obtinemus usque 
ad quantitates quinti ordinis 
[11] A*= ¿ —a jia+ T V6+TV7+iV/>p + i/p to+?) 
A-ih°{3qq — 2q q-\- 3 y Y) 
+-sV/°/°( 4 ^—^iiqqA-^qq— ngY)! 
Per operationes prorsus similes evolvimus 
[12] B* = B — a { T V a -f- i 6 + T V T + ttf"pV +1V9P ( 2 q + 4) 
+ i ¿° (4 q q — 4 q q'-\- 3 ? Y) 
— /o/°/° (2 pp + 8 q q — 8 q qA~ 11 $Y) i 
[13] C*=z C a j T V a H- tV ^ H - i 7 + tt/"pP + t\9P to + 2 # ) 
-h x ¿° (3 q q — 4 q ?'+ 4 $Y) 
— ¥V/°/ 0 (2pp + Wqq-ZqqA- 8 $Y) j 
Hinc simul deducimus, quum summa A*-\-B*-\~C* duobus rectis aequalis sit, 
excessum summae H-f-H-j-C supra duos angulos rectos, puta 
[14] A-\- B-\-C — TzA-v\\aA-i$A--*7-\-y'"ppA-Y9P{q-\-q) 
+(2 h°—i/°/°) q—qq ,J r qq)} 
Haec ultima aequatio etiam formulae i6] superstrui potuisset.