d $ cot a rr: ^^JLl^H — — ^ ^/ t^tl , cujus integrale esr 



cot. a iz: Const. — y l±±^ -h log. tiiL^iU^Ji^ , 



quod cum evancscere debeat casu i? — a , nanciscimur 



(h cot. a = i/ ^if — t/ t^i^f -4- loe. (v^(fe-f- 4v)-Hy[>)/ a 



/* ' i» ' 6 i^ o (-/(ftH-^a) -i-/6)yi; ' 



sive O cot a in >^'^'' ^^'^^^ y(b*^4u^ , j^^ (i/(&^ -^^^^i - fc) /a 



^ . 6 6 • *» a (y(6-i-4a)-t-y&) * 



§. aa. Arcus loxodromicus LM aequalis est arcui pa- 

 rabolico D M in sec. a ducto. Est autem arcus PM elementum 



cujus integrale reperitur 



P M — 0- — Moz. /ffe^4r^+2V -» _^ illLiillil l/ v, 



Ubi si substituitur i; zi: P C ~ a , nascitur arcus parabolicus 

 P P — - log. ^(^»^4^^ -2/0 ^ >1L^^11^ 1/ a . 



Unde sequitur , csse P D — P M , seu arcum parabolicum 



DMz=|Iog.2il^_lilJi2:if4-i ]/(ab-4-4aa) - l\/ (bv-^^vv). 



Quae expressio in sec. a ducta praebet arcum loxodromicum 

 L M ~ ^ per latus rectum Parabolae b , angulum rhombi o, at- 

 que rectas PC~a, PN — i?, quibus locorum L, M, situs de- 

 terminatur. 



$. a^. Pro area invenienda habemus (§. 21. 5.) 



z a z / (1-4- 3') ^ -9-"-^c^'---4fc.,) ^ 



eujus integrale ita determinatum , ut casu v zzi a evanescat, re- 



peritur ziz - — — — — -L_^'. / 0- 



la ■ -^ 



Quo 



