3 o MiJ :ellanea Curiofct. 



Lemma. 



The Legs of any plain Triangle continuing ; 

 if the Vertical Angle be augmented or 

 diminffid, by an Angle lefs than any 

 Angle ajJigrPd \ the Momenta or Inftan- 

 taneous Mutations of the Angles at the 

 Bafe, are to one another reciprocally, as 

 the Segments of the Bafe. 



At Fig. i. Plate 3. fuppofe the Triangle 

 ABC, whofe Vertex is A, its Legs AB, AC, 

 and Bafe BC, upon which let fall the Perpendi- 

 cular AD. Then let the Angle BAC be in- 

 creafed by the Indivifible Momentum CA i 9 and 

 let the Lines Bed, c D be drawn, which dif- 

 fer, in Imagination only, from the Lines BCD, 

 CD. Ifay, that the Momentum of the Angle 

 ABC (viz.. CBc) is to the Momentnm of the 

 Angle ACB or ACD, as CD to BD, that is 

 reciprocally as the Segments of the Bafe. 



DEMONSTRATION. 



Becaufe the Angle ACD, is the Sum of the 

 Angles ABC, BAC, its Momentum alfo mall 

 equal the Sum of the Momenta of thofe Angles ; 

 that is, it mail equal C A c -1- CBc But CAc 

 = CDc, fince, becaufe of the right Angle at 

 P, the Points A, D, C, c, are all in the Arch 

 of a Circle, whofe Diameter is AC : By EucL 

 3.9. And confequeiitly the Sum of the Angles 

 CBc, CDc (that is the Angle Dcd) mall be 

 the Momentum of the Angle ACD or ACB, 



But 



