Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1
SIMP. I ſaid ſo, and alſo confeſſe the reſt: and do now plainly
underſtand that the ſtone will not ſeparate from the Earth, for
that its receſſion in the beginning would be ſuch, and ſo ſmall,
that it is a thouſand times exceeded by the inclination which the
ſtone hath to move towards the centre of the Earth, which
tre in this caſe is alſo the centre of the wheel.
And indeed it muſt
be confeſſed that the ſtones, the living creatures, and the other
grave bodies cannot be extruded; but here again the lighter things
beget in me a new doubt, they having but a very weak propenſion
of deſcent towards the centre; ſo that there being wanting in
them that faculty of withdrawing from the ſuperficies, I ſee not,
but that they may be extruded; and you know the rule, that ad
deſtruendum ſufficit unum.
SAVL. We will alſo give you ſatisfaction in this. Tell me
therefore in the firſt place, what you underſtand by light matters,
that is, whether you thereby mean things really ſo light, as that
they go upwards, or elſe not abſolutely light, but of ſo ſmall
vity, that though they deſcend downwards, it is but very ſlowly;
for if you mean the abſolutely light, I will be readier than your
SIMP. I ſpeak of the other ſort, ſuch as are feathers, wool,
ton, and the like; to lift up which every ſmall force ſufficeth:
yet nevertheleſſe we ſee they reſt on the Earth very quietly.
SALV. This pen, as it hath a natural propenſion to deſcend
wards the ſuperficies of the Earth, though it be very ſmall, yet I
muſt tell you that it ſufficeth to keep it from mounting upwards:
and this again is not unknown to you your ſelf; therefore tell me
if the pen were extruded by the Vertigo of the Earth, by what
line would it move?
SIMP. By the tangent in the point of ſeparation.
SALV. And when it ſhould be to return, and re-unite it ſelf to
the Earth, by what line would it then move?
SIMP. By that which goeth from it to the centre of the
Earth.
SALV. So then here falls under our conſideration two
ons; one the motion of projection, which beginneth from the
point of contact, and proceedeth along the tangent; and the
ther the motion of inclination downwards, which beginneth from
the project it ſelf, and goeth by the ſecant towards the centre; and
if you deſire that the projection follow, it is neceſſary that the
petus by the tangent overcome the inclination by the ſecant: is it
not ſo?
SIMP. So it ſeemeth to me.
SALV. But what is it that you think neceſſary in the motion
of the projicient, to make that it may prevail over that