1degrees. Which may the better be ſeen, by hanging two weights
at two ſtrings of equal length, and then removing them from
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
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
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
ever other place; an accident truly wonderfull. We may add
another accident no leſs ſtrange than this, which is, That
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
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
ing by B. C. although it do ſublend but one ſole degree, or a
ſer Arch. Let us add the other wonder, which is, That the
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.
at two ſtrings of equal length, and then removing them from
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
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
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
ever other place; an accident truly wonderfull. We may add
another accident no leſs ſtrange than this, which is, That
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
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
ing by B. C. although it do ſublend but one ſole degree, or a
ſer Arch. Let us add the other wonder, which is, That the
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.
Two particular
notable accidents
in the penduli and
their vibrations.
notable accidents
in the penduli and
their vibrations.