Archimedes Texts

106
swer, that of infinite one part is not greater than another, since

both are infinite; nor can it be said, that of the infinite number,
an hundred thousand is a greater part than two, though that be
fifty thousand times greater than this; and if to the moving of
the Universe there be required a finite power, though very great
in comparison of that which sufficeth to move the Earth onely;
yet is there not implied therein a greater part of the infinite power,
nor is that part lesse infinite which remaineth unimploy'd. So that
to apply unto a particular effect, a little more, or a little lesse
power, importeth nothing; besides that the operation of such
vertue, hath not for its bound or end the Diurnal Motion onely;
but there are several other motions in the World, which we
know of, and many others there may be, that are to us unknown.
Therefore if we respect the Moveables, and granting it as out of
question, that it is a shorter and easier way to move the Earth,
than the Universe; and moreover, having an eye to the so many
other abreviations, and facilities that onely this way are to be ob
tained, an infallible Maxime of Aristotle, which he teacheth us,
that, frustra fit per plura, quod potest fieri per pauciora, ren
dereth it more probable that the Diurnal Motion belongs to the
Earth alone, than to the Universe, the Earth subducted.

Of infinity one
part is no bigger
than auother, al
though they are
comparatively un
equal.

SIMPL. In reciting that Axiom, you have omitted a small
clause, which importeth as much as all the rest, especially in our
case, that is to say, the words æquè bene. It is requisite therefore
to examine whether this Hypothesis doth equally well satisfie in all
particulars, as the other.

SALV. The knowledg whether both these positions do æquè
bene, satisfie, may be comprehended from the particular exami
nation of the appearances which they are to satisfie; for hitherto
we have discoursed, and will continue to argue ex hypothesi,
namely, supposing, that as to the satisfaction of the appearances,

both the assumptions are equally accomodated. As to the clause
which you say was omitted by me, I have more reason to suspect
that it was superfluously inserted by you. For the expression æquè
bene, is a relative that necessarily requireth two terms at least,
for a thing cannot have relation to its self, nor do we say, v. gr.
rest to be equally good, as rest. And because, when we say, that
is done in vain by many means, which may be done with fewer,
we mean, that that which is to be done, ought to be the same
thing, not two different ones; and because the same thing can
not be said to be done as well as its self; therefore, the addition
of the Phrase æquè bene is superfluous, and a relation, that hath
but one term onely.

In the Axiome
Frustra fit per plu
ra, &c. the addi
tion of æque benè,
is superfluous.

SAGR. Unlesse you will have the same befal us, as did yester
day, let us return to our matter in hand; and let Simplicius be