the lines themſelves PD, QD, generated by thoſe increments, will be as the ſines of incidence and emergence to each other, and é contra.
Proposition XCVIII. Problem XLVIII.
The ſame thing ſuppoſed, if round the axis AB (Pl. 25. Fig. 10) any attractive ſuperficies be deſcribed as CD, regular or irregular, through which the bodies iſſuing from the given place A muſt paſs; it is required to find a ſecond attractive ſupercies EF, which may make thoſe bodies converge to a given place B.
Let a line joining AB cut the firſt ſuperficies in C and the ſecond in E, the point D being taken any how at pleaſure. And ſupposing the ſine of incidence on the firſt ſuperficies to ſ of emergence from the ſame, and the ſine of emergence from the ſecond ſuperficies to the fine of incidence on the ſame, to as any given quantity M to another given quantity N; then produce AB to G, ſo that BG may be to CE as M - N to N; AD to H, ſo AH may be equal to AG; and DF to K ſo tha DK may be to DH as N to M. Join KB, and about the centre D with the interval DH deſcribe a circle meeting KB produced in L, and raw BF parallel to DL; and the point F will couch the line EF, which being turned round the axis AB will deſcribe the ſuperficies ſought. Q. E. F.
For conceive the lines CP, CQ to be every where perpendicular to AD, DF and the lines ER, ES
