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

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1may have erred in rehearſing his Argument, and to avoid running
into the ſame miſtakes for the future, I could wiſh I had his
Book; and if you had any body to ſend for it, I would take it
for a great favour.
SAGR. You ſhall not want a Lacquey that will runne for it
with all ſpeed: and he ſhall do it preſently, without loſing any
time; in the mean time Salviatus may pleaſe to oblige us with his
computation.
SIMP. If he go, he ſhall finde it lie open upon my Desk,
together with that of the other Author, who alſo argueth
gainſt Copernicus.
SAGR. We will make him bring that alſo for the more
tainty: and in the interim Salviatus ſhall make his calculation: I
have diſpatch't away a meſſenger.
SALV. Above all things it muſt be conſidered, that the motion
of deſcending grave bodies is not uniform, but departing from

reſt they go continually accelerating: An effect known and
ſerved by all men, unleſſe it be by the forementioned modern
thour, who not ſpeaking of acceleration, maketh it even and
niforme.
But this general notion is of no avail, if it be not known
according to what proportion this increaſe of velocity is made; a
concluſion that hath been until our times unknown to all
phers; and was firſt found out & demonſtrated by the ^{*} Academick,

our common friend, who in ſome of his ^{*} writings not yet

ed, but in familiarity ſhewn to me, and ſome others of his
quaintance he proveth, how that the acceleration of the right
tion of grave bodies, is made according to the numbers uneven
beginning ab unitate, that is, any number of equal times being
ſigned, if in the firſt time the moveable departing from reſt ſhall

have paſſed ſuch a certain ſpace, as for example, an ell, in the
cond time it ſhall have paſſed three ells, in the third five, in the
fourth ſeven, and ſo progreſſively, according to the following odd
numbers; which in ſhort is the ſame, as if I ſhould ſay, that the
ſpaces paſſed by the moveable departing from its reſt, are unto

each other in proportion double to the proportion of the times,
in which thoſe ſpaces are meaſured; or we will ſay, that the
ſpaces paſſed are to each other, as the ſquares of their times.
An exact
pute of the time of
the fall of the
non bullet from the
Moons concave to
the Earths centre.
* The Author.
* By theſe
tings, he every
where meanes his
Dialogues, De
tu, which I promiſe
to give you in my
ſecond Volume.
Acceleration of
the natural motion
of grave bodies is
the odde numbers
beginning at unity.
The ſpaces paſt
by the falling
grave body are as
the ſquares of their
times.
SAGR. This is truly admirable: and do you ſay that there is
a Mathematical demonſtration for it?
SALV. Yes, purely Mathematical; and not onely for this, but
for many other very admirable paſſions, pertaining to natural
tions, and to projects alſo, all invented, and demonſtrated by Our

Friend, and I have ſeen and conſidered them all to my very great
content and admiration, ſeeing a new compleat Doctrine to ſpring
up touching a ſubject, upon which have been written hundreds of