Archimedes Texts

412
degrees. Which may the better be seen, by hanging two weights
at two strings of equal length, and then removing them from per
pendicularity, one a little way, and the other very far; the which
being set at liberty, will go & return under the same times, the one
by arches very small, & the other by very great ones, from whence
followeth the conclusion of an admirable Problem; which is,

That a Quadrant of a Circle being given (take a little diagram of
the same, [in Fig. 3.]) as for instance: A B erect to the Hori
zon, so as that it rest upon the plain touching in the point B. and
an Arch being made with a Hoop well plained and smoothed in
the concave part, bending it according to the curvity of the Cir
cumference A D B. So that a Bullet very round and smooth
may freely run to and again within it (the rim of a Sieve is very
proper for the experiment) I say, that the Bullet being put in any
what ever place, neer or far from the lowest term B. As for in
stance, putting it in the point C, or here in D, or in E; and then
let go, it will in equal times, or insensibly different arrive at the
term B, departing from C, or from D, or from E, or from what
ever other place; an accident truly wonderfull. We may add
another accident no less strange than this, which is, That more
over by all the cords drawn from the point B to the points C,
D, E; and to any other whatsoever, taken not onely in the Qua
drant B A, but in all the whole circumference of the Circle the
said moveable shall descend in times absolutely equal; insomuch
that it shall be no longer in descending by the whole Diameter
erect perpendicularly upon the point B, then it shall in descend
ing by B. C. although it do sublend but one sole degree, or a les
ser Arch. Let us add the other wonder, which is, That the mo
tions of the falling bodies made by the Arches of the Quadrant
A B; are made in shorter times than those that are made by the
cords of those same Arches; so that the swiftest motion, and
made by a moveable in the shortest time, to arrive from the
point A, to the term B, shall be that which is made, not by the
right line A, B, (although it be the shortest of all those that can
de drawn between the points A. B.) but by the circumference
A D B. And any point being taken in the said Arch; as for
example: The point D. and two cords drawn A D, and D. B.
the moveable departing from the qoint A, shall in a less time
come to B, moving by the two cords A D and D B. than by the
sole cord A, B. But the shortest of all the times shall be that of
the fall by the Arch A D B. And the self same accidents are
to be understood of all the other lesser Arches taken from the
lowermost term B. upwards.

Admirable Pro
blems of movea
bles descending by
the Quadrant of a
Circle, and of those
descending by all
the cords of the
whole Circle.

SAGR. No more, no more; for you so confund and fill me
with Wonders, and distract my thoughts so many several wayes,