BOOK III.] OF NATURAL PHILOSOPHY. 47 PROPOSITION XLL PROBLEM XXI. Prom three observations given to determine the orbit of a comet moving in a parabola. This being a Problem of very great difficulty, I tried many methods of resolving it ; and several of these Problems, the composition whereof I have triven in the first Book, tended to this purpose. But afterwards I contrived the following solution, which is something more simple. •Select three observations distant one from another by intervals of time nearly equal ; but let that interval of time in which the comet moves more slowly be somewhat greater than the other ; so, to wit, that the dif ference of the times may be to the sum of the times as the sum of the At imes to about 600 days ; or that the point E may fall upon M nearly, and may err therefrom rather towards 1 than towards A. If such direct observations are not at hand, a new place of the comet must be found, by Lem. VI. Let S represent the sun ; T, t, r} three places of the earth in the orbis mag-mis; TA, /B, rC, three observed longitudes of the comet; V the time between the first observation and the second ; W the time between the second and the third ; X the length which in the whole time V + W the comet might describe with that velocity which it hath in the mean distance of the earth from the sun, which length is to be found by Cor. 3,