1^ Atti 



A B j AC ad idem peripheriae pun£lum fubtendunt , a G 

 ad M tranfcundo augeatur , ac deinde imminuatur ufque 

 ad L , in punftis M , & N fibi proximis nec augeri , nec 

 minili debct eadem differentia, five ede debet BMA^ — AMG 

 =:^BNA — ANC. Eli: porro externus angulus NQA1 = NBM 

 -+CMA = BNA-fNAM, five eft NBM-^ BMA — BNA 

 r=NAM, atque eù pariter angulus NPA1= NCM -+ ANG 

 ^ AMG -+ NAM , five eft NGM -^ ANC — AMG = N AM. 

 Iraque ob BAIA — AMG — BNA -h- ANC =o ; in loco ma- 

 ximae angulorum eorumdeni diftèrentiae erir NBM -+ NGM 

 = 2 NAM. Hoc dato radiis BM , GN defcribanrur arcus 

 MO, NT, atque ex punftis B, G ducantur in radios AM, 

 AN perpendicula BD, CE. Ob reclos angulos BMO , AMN 

 aequales erunt anguli BMD, OMN .-atque ob reftos fimiliter angu- 

 los D , O fimib'a crunt triangula MNO, MBD , eritque MN : MO 

 = MB : MD. Pariter erunt limilia triangula MNT, CNE , eritque 

 MN: NT = NC: NE. lam vero ob punfta M, N fibi pro- 

 xima» erit NG=cMG, & AD=^AE: atque ob iimilitudinem 



triangulorum BAD, MAH, erit A D = A E = ^^ » 



,,_ AG'— AB-AH - ^-rr- AG'-fAB.AH j^ ■ • 



M D = ^ „ , & N E = --, „ Erit ita- 



A G AG 



que arcus M O = t^-JLl^^JL M N , & angulus NBM 



^ AG.BM " 



^ ag'-Ta^. ah ^^ n ac pariter angulus N C M = 



AG. BM' r o 



f^'JlL^^-AI? M N: 8c cnm bini fimul hi anguli acquari 



AG. e M' 



dcbeant duplo angulo NiVM, fcu^^, prodibit 2 B M\ 



C M= = A G^^=^A B. A H. C M^ -+ A G -r A B. A H. B M\ 

 At in triangulo M A B eft B M' = A G=-f A B'— 2 A M. 

 A D = A G' -+- A B'— 2 A B. A H , ac pariter efl G M^ = 



AG' 



