§. 2*7- 1*^0 area LjPM nz S' invenienda liabenHis 

 m » = i|i , M n = u, 5 Cp, proinde M n 7m y — ' 338' = !iii^3^^ 

 et MVm~dS'=: <"^-°="^^ — '"^-^'=""^' tan^. c., qua formula 

 sic inte|;rata , ut .casu u :zz: 6 fvaAescat, nancisciinur areaixi 



L P M — ^' •-!= ^s-i? (ilizii! - a' (6 — u) ). 

 Sin autem area L D M ~ S desideratur, areolam D Mm d z^ dS 

 loco eieraenti MPm investigare oportet, quem in fineni diffejrcntiale 

 Mnmv ^dd S zn lil-^Jii$ sic est integrandum, ut casu a ~ 6 



€yanes.cat , praej:erea.que negative accipiendum ;, qupniam cres- 

 cente u area D M m d decrescit. Habemus itaque 



DMmdi:rdS=:'M=^^ -- i_v3-63)3n ^ . 



cpjus integrale cum casu a ~ 6 evanescere debeat , repcrituj: 



L M P = ? =: l^^Jl (6^ (i, - U) -^ eir-Jf^) , 

 Duabus his areis S, S^, in summam redactis, resultat are^a solidi 

 L P D zn l^sj? (h -r- u) (L' a') — ^2rz^ (f) j 



3ai;^ ' ^ ' 3a^' 



ideoque posito (finzaTr, integra solidi superficies — ?-^ (6^— a^), 

 ubi est 6 radius basis. Quare cum sit area sectoris LCD z *1$ 3 P. 

 area basis —; fe' tt i^ XL, erit area L P D — lii!;^!:!^ P , inte- 

 griquc area solidi — ?. '^^~ ii^Q^. 



Area itaq«e sblidi, quod e revolutionc curvae fiujus circum 

 laxem nascitu^ , a qnadr^tura cir^ uli d^pendet. RectificatiD vero 

 curvae et Loxodromiae in solido descrjptae , aon minus quam 

 quadratura algebraice assignari pote^t, concessa scilicet ejus con- 

 structionc vel da|o anguio con^tante ot^ 



