as ) ° c 
1 5 X 
antur, & ÀGD ut pofitivus accipiatur, erit ex op- 
pofitione arcus AC negativus, chorda etiam AD 
erit pofitiva , & AC negativa, unde dato AD = 
ArV^ax, erit AC = — Vi ax, adeo ut variante fun- 
damento, five hypothefi Problematum j applicatio 
fignorum etiam variare posfit. 
' 5 . 6 . 
Quoniam chordæ arcuum circularium ut Ve- 
flores circulos defcribentes confiderari posfunt, par- 
tes Veftorum pofitivæ & negativae probe inprimis 
diftingvendæ erunt in multifeflione arcuum vel 
angulorum , cujus theoria , praelucente rf Alember- 
to, jam illuftranda venit. Antequam vero illam 
ordiar ex theoremate fin ( A -f - B) — -h CoCA fin B 
-f-fin^Cofi9 regulam deducam angulum quem- 
cunque multiplicandi: fit B—x, A—mx , erit 
Sin m “h i . X =. Cofx fin mx -f- Cof mx fin x 
fin m — i . x = Cofx fin mx — Cofwx fin x, adeoque 
Sin m -f- i . x +fin m — I . x = 2 Cofx fin mx 
Sin m -+• t . x = aCofx fin mx — fin m — 1 .x. Hinc 
Si m = 0 erit fin x = — fin ( — x ) = fin x 
»2 = 1-- fin 2x — 2 Cofx fin x 
m — 2 - - fin 3x = 4 Cofx 2 finx — fin x 
= 3 fin x — 4 fin x 3 
m — 3 - - fin qx = 2 Cofx ( 3 fin x — 4 fin x 3 J 
— 2 Cofx fin x 
= 2 Cofx ( 2 fin x • — 4 fin x 3 ) 
= Co f x (4 finx — 8 fin x 3 ) 
m = 4 - - fin 5x = 2 Cofx 2 (4 fin x — 8 fio x 3 ) 
— 3 fin x + 4 fin .x 3 ) 
= 5 fin x — 20 finx 3 -f- 16 fin x* 
& fie porro, quod ultra recenfere inutile cenfeo, 
cum 
