Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667
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1tion, from which enſueth the ſeparation and elongation of the
pen from the Earth?
SIMP. I cannot tell.
SALV. How, do you not know that? The moveable is here
the ſame, that is, the ſame pen; now how can the ſame moveable
ſuperate and exceed it ſelf in motion?
SIMP. I do not ſee how it can overcome or yield to it ſelf in
motion, unleſſe by moving one while faſter, and another while
ſlower.
SALV. You ſee then, that you do know it. If therefore the
projection of the pen ought to follow, and its motion by the
gent be to overcome its motion by the ſecant, what is it requiſite
that their velocities ſhould be?
SIMP. It is requiſite that the motion by the tangent be greater
than that other by the ſecant.
But wretch that I am! Is it not
only many thouſand times greater than the deſcending motion of
the pen, but than that of the ſtone?
And yet like a ſimple fellow
I had ſuffered my ſelf to be perſwaded, that ſtones could not be
extruded by the revolution of the Earth.
I do therefore revoke
my former ſentence, and ſay, that if the Earth ſhould move,
ſtones, Elephants, Towers, and whole Cities would of neceſſity be
toſt up into the Air; and becauſe that that doth not evene, I
clude that the Earth doth not move.
SALV. Softly Simplicius, you go on ſo faſt, that I begin to be
more afraid for you, than for the pen.
Reſt a little, and obſerve what
I am going to ſpeap.
If for the reteining of the ſtone or pen
nexed to the Earths ſurface it were neceſſary that its motion of
deſcent were greater, or as much as the motion made by the
gent; you would have had reaſon to ſay, that it ought of neceſſity
to move as faſt, or faſter by the ſecant downwards, than by the
tangent Eaſtwards: But did not you tell me even now, that a
thouſand yards of diſtance by the tangent from the contact, do
remove hardly an inch from the circumference?
It is not
ent therefore that the motion by the tangent, which is the ſame
with that of the diurnall Vertigo, (or haſty revolution) be fimply
more ſwift than the motion by the ſecant, which is the ſame with
that of the pen in deſcending; but it is requiſite that the ſame be
ſo much more ſwift as that the time which ſufficeth for the pen
to move v.g. a thouſand yards by the tangent, be inſufficient for
it to move one ſole inch by the ſecant.
The which I tell you ſhall
never be, though you ſhould make that motion never ſo ſwift,
and this never ſo ſlow.
SIMP. And why might not that by the tangent be ſo ſwift, as
not to give the pen time to return to the ſurface of the Earth?
SALV. Try whether you can ſtate the caſe in proper termes,