Archimedes Texts

SALV. And have you no other conceit thereof than this?

SIMPL. This I think to be the proper definition of equal mo
tions.

Velocities are said
to be equal, when
the spaces passed
are proportionate to
their time.

SAGR. We will add moreover this other: and call that equal
velocity, when the spaces passed have the same proportion, as the
times wherein they are past, and it is a more universal definition.

SALV. It is so: for it comprehendeth the equal spaces past in
equal times, and also the unequal past in times unequal, but pro
portionate to those spaces. Take now the same Figure, and apply
ing the conceipt that you had of the more hastie motion, tell me
why you think the velocity of the Cadent by C B, is greater
than the velocity of the Descendent by C A?

SIMPL. I think so; because in the same time that the Cadent
shall pass all C B, the Descendent shall pass in C A, a part less
than C B.

SALV. True; and thus it is proved, that the moveable moves
more swiftly by the perpendicular, than by the inclination. Now
consider, if in this same Figure one may any way evince the o
ther conceipt, and finde that the moveables were equally swift
by both the lines C A and C B.

SIMPL. I see no such thing; nay rather it seems to contradict
what was said before.

SALV. And what say you, Sagredus? I would not teach you
what you knew before, and that of which but just now you pro
duced me the definition.

SAGR. The definition I gave you, was, that moveables may
be called equally swift, when the spaces passed are proportional
to the times in which they passed; therefore to apply the defini
tion to the present case, it will be requisite, that the time of de
scent by C A, to the time of falling by C B, should have the
same proportion that the line C A hath to the line C B; but I
understand not how that can be, for that the motion by C B is
swifter than by C A.

SALV. And yet you must of necessity know it. Tell me a little,
do not these motions go continually accelerating?

SAGR. They do; but more in the perpendicular than in the
inclination.

SALV. But this acceleration in the perpendicular, is it yet not
withstanding such in comparison of that of the inclined, that
two equal parts being taken in any place of the said perpendicu
lar and inclining lines, the motion in the parts of the perpendicu
lar is alwaies more swift, than in the part of the inclination?

SAGR. I say not so: but I could take a space in the inclinati
on, in which the velocity shall be far greater than in the like space
taken in the perpendicular; and this shall be, if the space in the