Archimedes Texts

206
of the accelerated degrees of velocity, answering to the triangle
A B C, hath passed in such a time such a space, it is very reasonable
and probable, that making use of the uniform velocities answering
to the parallelogram, it shall passe with an even motion in the
same time a space double to that passed by the accelerate mo
tion.

SAGR. I am entirely satisfied. And if you call this a probable
Discourse, what shall the necessary demonstrations be? I wish
that in the whole body of common Philosophy, I could find one
that was but thus concludent.

SIMP. It is not necessary in natural Philosophy to seek exqui
site Mathematical evidence.

SAGR. But this point of motion, is it not a natural question?
and yet I cannot find that Aristotle hath demonstrated any the
least accident of it. But let us no longer divert our intended
Theme, nor do you fail, I pray you Salviatus, to tell me that
which you hinted to me to be the cause of the Pendulum's qui
escence, besides the resistance of the Medium ro penetration.

SALV. Tell me; of two penduli hanging at unequal distan
ces, doth not that which is fastned to the longer threed make its
vibrations more seldome?

The pendulum
hanging at a long
er threed, maketh
its vibrations more
seldome than the
pendulum hanging
at a shorter threed.

SAGR. Yes, if they be moved to equall distances from their
perpendicularity.

SALV. This greater or lesse elongation importeth nothing at
all, for the same pendulum alwayes maketh its reciprocations in e
quall times, be they longer or shorter, that is, though the pendulum

be little or much removed from its perpendicularity, and if they
are not absolutely equal, they are insensibly different, as expe
rience may shew you: and though they were very unequal, yet
would they not discountenance, but favour our cause. There
fore let us draw the perpendicular A B [in Fig. 9.] and hang from
the point A, upon the threed A C, a plummet C, and another up
on the same threed also, which let be E, and the threed A C, being
removed from its perpendicularity, and then letting go the plum
mets C and E, they shall move by the arches C B D, E G F, and
the plummet E, as hanging at a lesser distance, and withall, as
(by what you said) lesse removed, will return back again faster,
and make its vibrations more frequent than the plummet C, and
therefore shall hinder the said plummet C, from running so much
farther towards the term D, as it would do, if it were free: and
thus the plummet E bringing unto it in every vibration continuall

impediment, it shall finally reduce it to quiescence. Now the
same threed, (taking away the middle plummet) is a composition
of many grave penduli, that is, each of its parts is such a pendu
lum fastned neerer and neerer to the point A, and therefore dispo