&1 DE rNCFLIS CYLINDRORrm 



ABxBO, akitudo Aiitcm ^r. Eft itaque Vngula prior 

 tid hiinc in mtionc 1 6 ad 15. 



§ 13. Pro (upcrficicbus hinim Vngiilarum refu- 

 matur acquatio §. 11. a — x—y'^^ ne autem calculus 

 euadat nimis molellus, alTumamus tantum, pro Para- 

 bola Yulgari, a — x—j', erit itaque V ( r/.r - -f-^j-) 

 :=djV{^y--\-i), hinc v = .vVC^a- -{-«>= )rr 



{ady~y-dy)V{^y--\-i )— ^[^y^.^\ ) — 



^'^^'J(Xy^Tf~~\ cuiub Intcgrale vthabeatur, pa- 

 no illud appariturum cflc fub hac forma («>'— pj^) 

 y ( ^y- -4- I ) _|- y/y-—^-^ ; fada diffcrentiatione hu- 

 ius e.xpreirionis , ct tcrminis homologis comparatis, in- 

 licnitur a — — 5-5 — , p~^, y— — j^-'~-> quibus lub- 

 flitntis oritiir : S == f ( '^^T'j - i/ ^ ) "^' ( 4-J'' H- 1 ) - 



~3l^~*^vl+3'^H^~^ '+'*^"'^'"''^'^ diqua. Scd notum eft, 

 jncmbrum huius aequationis inintcgrabilc dcpcndcrc a 

 Qiiadi-atura Hy.perbolae^ quarc etiam luperiicici huius 

 Vngiilaris Qiiadratura ab cadcm pcndet. 



§. 14.. Pro fupcriicie vcro Vngulac Pai-aboHcie 



per axem afTumo .viz: j-, vnde V {dx--{-dy- ) zzdy 



y(4./2_|_i)^ et ~=yV{dx--^-dy-)—ydyV{^ 



j^-hi), quae aequatio fic integrata, vt pi^fito yzzo 



^ ■■ r c{^y --\-i )-- c ; 

 fiat .f~c>, efficit fequentcm : .fzn — — ; 



ex quo apparcr, liaiic Vngulam per axem Gcomerri- 

 icam haberc fupcriiciem , quac , pofitoj— /', integra 



,. c{^b- -\-i)^ — c 



cuadit — -IZ ! 



i:ib 



§. 15. 



