1and I will give you an anſwer. Tell me therefore, how much do

you think ſufficeth to make that motion ſwifter than this?

you think ſufficeth to make that motion ſwifter than this?

SIMP. I will ſay for example, that if that motion by the

gent were a million of times ſwifter than this by the ſecant, the

pen, yea, and the ſtone alſo would come to be extruded.

gent were a million of times ſwifter than this by the ſecant, the

pen, yea, and the ſtone alſo would come to be extruded.

SALV. You ſay ſo, and ſay that which is falſe, onely for

want, not of Logick, Phyſicks, or Metaphyſicks, but of

try; for if you did but underſtand its firſt elements, you would

know, that from the centre of a circle a right line may be drawn

to meet the tangent, which interſecteth it in ſuch a manner, that

the part of the tangent between the contact and the ſecant, may

be one, two, or three millions of times greater than that part of

the ſecant which lieth between the tangent and the circumference,

and that the neerer and neerer the ſecant ſhall be to the contact,

this proportion ſhall grow greater and greater in infinitum; ſo

that it need not be feared, though the vertigo be ſwift, and the

motion downwards ſlow, that the pen or other lighter matter can

begin to riſe upwards, for that the inclination downwards always

exceedeth the velocity of the projection.

want, not of Logick, Phyſicks, or Metaphyſicks, but of

try; for if you did but underſtand its firſt elements, you would

know, that from the centre of a circle a right line may be drawn

to meet the tangent, which interſecteth it in ſuch a manner, that

the part of the tangent between the contact and the ſecant, may

be one, two, or three millions of times greater than that part of

the ſecant which lieth between the tangent and the circumference,

and that the neerer and neerer the ſecant ſhall be to the contact,

this proportion ſhall grow greater and greater in infinitum; ſo

that it need not be feared, though the vertigo be ſwift, and the

motion downwards ſlow, that the pen or other lighter matter can

begin to riſe upwards, for that the inclination downwards always

exceedeth the velocity of the projection.

SAGR. I do not perfectly apprehend this buſineſſe.

SALV. I will give you a moſt univerſal yet very eaſie demon

ſtration thereof. Let a proportion be given between B A [in Fig.

3.] and C: And let B A be greater than C at pleaſure. And let

there be deſcribed a circle, whoſe centre is D. From which it is

required to draw a ſecant, in ſuch manner, that the tangent may

be in proportion to the ſaid ſecant, as B A to C. Let A I be

ſuppoſed a third proportional to B A and C. And as B I is to

I A, ſo let the diameter F E be to E G; and from the point G,

let there be drawn the tangent G H. I ſay that all this is done as

was required; and as B A is to C, ſo is H G to G E. And in

gard that as B I is to I A, ſo is F E to E G; therefore by

ſition, as B A is to A I; ſo ſhall F G be to G E. And becauſe C

is the middle proportion between B A and A I; and G H is a

middle term between F G and G E; therefore, as B A is to C,

ſo ſhall F G be to G H; that is H G to G E, which was to be

demonſtrated.

A geometrical

demonſtration to

prove the

bility of extruſion

by means of the

terreſtrial vertigo.

demonſtration to

prove the

bility of extruſion

by means of the

terreſtrial vertigo.

SAGR. I apprehend this demonſtration; yet nevertheleſſe, I

am not left wholly without hæſitation; for I find certain

ſed ſcruples role to and again in my mind, which like thick and

dark clouds, permit me not to diſcern the cleerneſſe and neceſſity

of the concluſion with that perſpicuity, which is uſual in

matical Demonſtrations. And that which I ſtick at is this. It is

true that the ſpaces between the tangent and the circumference do

gradually diminiſh in infinitum towards the contact; but it is alſo

true on the contrary, that the propenſion of the moveable to

am not left wholly without hæſitation; for I find certain

ſed ſcruples role to and again in my mind, which like thick and

dark clouds, permit me not to diſcern the cleerneſſe and neceſſity

of the concluſion with that perſpicuity, which is uſual in

matical Demonſtrations. And that which I ſtick at is this. It is

true that the ſpaces between the tangent and the circumference do

gradually diminiſh in infinitum towards the contact; but it is alſo

true on the contrary, that the propenſion of the moveable to