Mijcetlanea Curio fa. 



An In fiance of the Excellence of the 

 Modern Algebra, in the Refolu- 

 tion of the Problem of finding the 

 Foci of Optic k Glaffes Vniver- 

 fally. By E. Halley, $< R. S. 



V I ' 1 H E Excellence of the Modern Geometry 

 JL is in nothing more evident , than in 

 thofe full and adequate Solutions it gives to 

 Problems ; reprefenting all the poffible Cafes 

 at one view, and in one general Theorem, 

 many times comprehending whole Sciences ; 

 •which deduced at length into Proportion?, 

 and demonftrated after the manner of the 

 Ancients, might well become the Subjects of 

 large Treadles : For whatfoever Theorem 

 fblves the raoft complicated Problem of the 

 kind, does with a due Reduction reach all the 

 fubordinate Cafes. Of this I now defign to 

 give a notable Inftance in the Do£h*ine of 

 Dioptricks. 



This Dioptnck Problem is, that of finding 

 the Focus of any fort of Lens, expofed either 

 to converging,- diverging, or parallel Rays of 

 Light, proceeding from, or tending to a gi« 

 ven Point in the Axis of the Lens, be the I{a* 

 tio of I{ef raft ion what it will, according to the 

 Nature of the tranfparent Material whereof 

 the Lens is formed, and alfo with allowance 

 for the thicknefs of the Lens between the Ver- 

 tices 



