Mifcettanea Curiofa. 349 



tkcs of the two Spherical Segments. This Pro- 

 blem being folved in one Cafe, mutatis mutan* 

 Ms, will exhibit Theorems for all the pofiible 

 Cafes, whether the Lens be Double-Convex or 

 Double-Concave, Piano-Convex, or Piano* Concave* 

 or Convexo-Concave* which fort are ufually call'd 

 Menifei. But this only to be underftood of thofe 

 Beams which are neareft to the Axis of the Lcnt% 

 fo as to occafion no fenfible difference by their 

 Inclination thereto ; and the Fccus here formed-, 

 is by Dioptric]^ Writers commonly calFd the 

 principal Focus, being that^of ufe in Telefcofcs 

 and Microfcopes. 



Let then (in Fig. 7. Tab, f.) BE, 6 be a dou- 

 ble Convex Lens, C the Center of the Seg- 

 ment EB, and K the Center of the Segment 

 E0, B£ the thicknefs of the Lens, D a Point 

 in the Axis of the Lens ; and it is required to 

 find the Point F, at which the Beams proceed- 

 ing from the Point D, are collected therein, the 

 J{atio of Refraction being as m to n. Let the 

 diftanceof the Objeft DB=r.DA=</ (the Point 

 A being fuppofed the fame with B, but taken 

 at a diftance therefrom, to prevent the coin- 

 cidence of fb many Lines) the Radius of the 

 Segment towards the Object; CB or C t\~-r, 

 and the Radius of the Segment from the Ob- 

 ject K# or K=:f ; and let B 0 the thicknefs of 

 the Lens be and then let the Sine of the 

 Angle of Ineidence D A G be to the Sine of the 

 refracted Angle HAG or CAf as rn to n : 

 And in very fmall Angles, the Angles themfelves 

 will be in the feme proportion ; whence it will 

 follow that, 



As 



