Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/438

 all conversion from the Annual motion, could be made, one while in a greater, and another while in a lesser proportion; which diversity, and no other thing, could be assigned for the cause of the alterations, Monethly and Annual, that are seen in the greatnesse of the Ebbings and Flowings. I will now consider how this proportion of the additions and substractions of the Diurnal Revolution, and Annual motion may grow greater and lesser three several wayes. One is by increasing and diminishing the velocity of the Annual motion, retaining the additions and substractions made by the Diurnal conversion in the same greatnesse, because the Annual motion being about three times greater, that is, more velocious than the Diurnal motion (considered likewise in the Grand Circle) if we increase it anew, the additions and substractions of the Diurnal motion will occasion lesse alteration therein: but, on the other side, making it more slow, it will be altered in greater proportion, by that same diurnal motion, just as the adding or substracting four degrees of velocity from one that moveth with twenty degrees, altereth his course lesse, than those very four degrees would do, added or substracted from one that should move onely with ten degrees. The second way would be, by making the additions and substractions greater and lesser, retaining the annual motion in the same velocity; which is as easie to be understood, as it is manifest, that a velocity v. gr. of 20 degr. is more altered by the addition or substraction of 10. deg. than by the addition or substraction of 4. The third way would be, in case these two were joyned together, diminishing the annual motion, & increasing the diurnal additions and substractions. Hitherto, as you see, it was no hard matter to attain, but yet it proved to me very hard to find by what means this might be effected in Nature. Yet in the end, I finde that she doth admirably make use thereof, and in wayes almost incredible: I mean, admirable and incredible to us, but not to her, who worketh even those very things, which, to our capacity, are of infinite wonder, with extraordinary facility and simplicity: and that which it is hard for us to understand, is easie for her to effect. Now to proceed, having shewn that the proportion between the additions and substractions of the Diurnal conversion and Annual motion may be made greater and lesser, two wayes, (and I say two, because the third is comprized in the two first) I adde, that Nature maketh use of them both: and farthermore, I subjoyn, that if she did make use but of one alone, it would be necessary to take away one of the two Periodical alterations. That of the Monethly Period would cease, if the annual motion should not alter. And in case the additions and substractions of the diurnal revolution should continually