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.

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.

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.

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.

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.

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.

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.

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

made according to

the odde numbers

beginning at unity.

the natural motion

of grave bodies is

made according to

the odde numbers

beginning at unity.

The ſpaces paſt

by the falling

grave body are as

the ſquares of their

times.

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?

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

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