Mtj :ellanea Curioja. 3 \ 

 But thofe Angles CB c, D c J 9 being indefinite- 

 ly i mall, are to one another as their oppofite 

 fides, that is, as c D or CD to BD, that is as 

 the Segments of the Bafe reciprocally. Q.: 

 E : D. 



If each of the Angles B and C be Acute, the 

 Lemma will ltill ( mutatis mutandis*) be demon- 

 ftrated after the fame Manner. 



COROLLARY. 



Hence it follows that the Momenta of the 

 Angles at the Bafe, are to one another direftly 

 as the Tangents of thofe Angles. 



By the Help of this Lemma, I will be eafie 

 to find the Diameter of any his whatfoever - 0 

 and that either by Calculation, or a Geometrical 

 Conftruftion. For taking any right Line, as 

 CA (F/>. 2.) let it be divided firft of all in 

 D, fo that CA, may be to CD, in the Ratio 

 of the Refra&ion in Water, which is as 250 

 to 187, or more accurately, as 529 to 396. 

 Then let CA be divided fo in E, that CE may 

 be to AE, as Unity to the Number of Reflexi- 

 ons, a Ray of the Sun (fit to produce the Iris 

 propofed) undergoes : And upon the Diame- 

 ter AE defcribing the Semi-Circle ABE, on 

 the Center C with the Radius CD defcribe the 

 Arch BD, meeting the Semi-Circle ABE in 

 the Point B. Laftly, Drawing the Right Lines 

 CB, AB, let CF be let fall perpendicular upon 

 AB produced, and EB parallel thereto. I fay 

 then, that CBF is the Angle of Incidence, and 

 CAB the Refraded Angle that we enquire af- 

 ter, and which will produce the Iris pro- 

 posal 



