Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/412

 320 to FB, FD repectively, and therefore QS to be always equal to CE; and (by cor. 2. prop. 97.) PD will be to QD as M to N, and therefore as DL to DK. or FB to FK; and by diviion as DL−FB or PH−PD−FB to FD or FQ−QD; and by compoition as PH−FB to FQ, that is, (becaue PH and CG, QS and CE are equal) as CE+BG−FR to CE−FS. But (becaue BG is to CE, as M−N to N) it comes to pas alo that CE+BG is to CE as M to N; and therefore, by diviion, FR is to FS as M to N; and therefore (by cor. 2. prop. 97.) the uperficies EF compels a body, falling upon it in the direction DF to go on in the line FR to the place B. Q. E. D.

In the ame manner one may go on to three or more uperficies. But of all figures the phærical is the mot proper for optical ues. If the object glaes of telecopes were made of two glaes of a phærical figure, containing water between them; it is not unlikely that the errors of the refractions made in the extreme parts of the uperficies of the glaes, may be accurately enough corrected by the refractions of the water. Such object-glaes are to be preferred before elliptic and hyperbolic glaes, not only becaue they may be formed with more eae and accuracy, but becaue the pencils of rays ituate without the axis of the glas would be more accurately refracted by them. But the different refrangibility of different rays is the real obtacle that hinders optics from being made perfect by phærical or any other figures. Unles the errors thence ariing can be corrected all the labour pent in correcting the others is quite thrown away.