]\difcelianea Curiofa. 229 



PRO f. IV, THEOREM. 



(Fig. 36.) The Space AGF contained un- 

 der the Catena ria AF, and the right 

 Lines FG, AG, parallel to AB, BF, 

 is equal to the Rett angle under the Se- 

 miaxis AC, and DH the difference of 

 the Ordinates in the Hyperbola and Ca- 

 tenaria, 



For DH ( == BH •==■ BD == by frif&jf 



ax-\-xx ax 

 tiort II. — — — - — « ~_— — ) 



— — . Wherefore the Fluxion of the 



\l Xax\x % 



Re&angle under the given Line AC and DH 



axx ax 

 (= — - — ■ — = x x — ■ — — — • x FG) 



== the Fluxion of the Space AFG, And 

 fince thefe Figures do arife both together, it 

 follows that the Re&angle under AG and 

 DH is equal to the Space AGF, Qj E : D. 



Q.5 COROL 



