Archimedes Texts

409
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 con
sider 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 dimi
nishing the velocity of the Annual motion, retaining the additi
ons 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 de
grees, 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 additi
ons and substractions greater and lesser, retaining the annual mo
tion 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 substra
ction 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 ea
sie for her to effect. Now to proceed, having shewn that the
proportion between the additions and substractions of the Diur
nal conversion and Annual motion may be made greater and les
ser, 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 Perio
dical 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