3 a Mtjcellanea Curiofa. 



. DEMONSTRATION. 



Becaufe the Triangles ACF, AEB are fimi- 

 lar, it will be AF: BF :: AC: EC; that is, 

 as the Number of Reflexions encreas'd by Uni- 

 ty to Unity (by the Conflrutlion) and confe- 

 quently the Momentum of the Angle CBF, will 

 be to the Momentum of the Angle CAF, in the 

 fame Proportion (by the foregoing Lemma.) 

 But the Sine of the Angle CBF, is to the 

 Sine of the Angle CAF, in the Proportion of 

 the Sides CA,CB, that is, in the Proportion 

 of the Refra&ion given (alfo by thz Conflrutlion.') 

 Therefore CAF is the Refra&ed Angle, cor- 

 refponding to the Angle of Incidence CBF} 

 and their Momenta are in the Ratio propos'd, 

 wherefore they are the Angles fought. Q. E. D. 



And now, multiplying the Refra&ed An- 

 gle by the Number of the Reflexions encreas'd 

 by Unity, and from the Produd fubftra&ing 

 the Angle of Incidence, we fhall have half the 

 Diftance of the Iris from the Sun, if the 

 Number of Reflexions be cve?j, or from the 

 Point oppofite to the Sun, if that Number be 

 uneven, as we have lhewn already. Hence 

 wc may exhibit (by a Coriftmttioh concife and 

 eloquent enough) the Incidencies of all the 

 Orders of Iris's^ in any Liquor whofe Refra- 

 ction is known. For if the Line AC (FIG. 2.) 

 be divided into Two equal Parts at E, into 

 Three equal Parts at % into Four at s, into 

 Five at 77, &c. And on the Diameter AE, Ae y 

 A*, An, be defcrib'd, the Semi-Circles ABE, 

 Abe, AiSfe, Aw, which are all interfered in 

 the Points B, b, 0, v 7 by the Arch DBfoV'de- 



fcrib'd 



