1amongſt thoſe who know nothing thereof. Now to ſhew you how

great their errour is who ſay, that a Sphere v.g. of braſſe, doth not

touch a plain v.g. of ſteel in one ſole point, Tell me what

ceipt you would entertain of one that ſhould conſtantly aver, that

the Sphere is not truly a Sphere.

great their errour is who ſay, that a Sphere v.g. of braſſe, doth not

touch a plain v.g. of ſteel in one ſole point, Tell me what

ceipt you would entertain of one that ſhould conſtantly aver, that

the Sphere is not truly a Sphere.

The truth

ſometimes gaines

ſtrength by

tradiction.

ſometimes gaines

ſtrength by

tradiction.

SIMP. I would eſteem him wholly devoid of reaſon.

SALV. He is in the ſame caſe who ſaith that the material Sphere

doth not touch a plain, alſo material, in one onely point; for to

ſay this is the ſame, as to affirm that the Sphere is not a Sphere.

And that this is true, tell me in what it is that you conſtitute the

Sphere to conſiſt, that is, what it is that maketh the Sphere differ

from all other ſolid bodies.

doth not touch a plain, alſo material, in one onely point; for to

ſay this is the ſame, as to affirm that the Sphere is not a Sphere.

And that this is true, tell me in what it is that you conſtitute the

Sphere to conſiſt, that is, what it is that maketh the Sphere differ

from all other ſolid bodies.

The sphere

though material,

toucheth the

rial plane but in

one point onely.

though material,

toucheth the

rial plane but in

one point onely.

SIMP. I believe that the eſſence of a Sphere conſiſteth in

ving all the right lines produced from its centre to the

rence, equal.

ving all the right lines produced from its centre to the

rence, equal.

The definition of

the ſphere.

the ſphere.

SALV. So that, if thoſe lines ſhould not be equal, there ſame

ſolidity would be no longer a ſphere?

ſolidity would be no longer a ſphere?

SIMP. True.

SALV. Go to; tell me whether you believe that amongſt the

many lines that may be drawn between two points, that may be

more than one right line onely.

many lines that may be drawn between two points, that may be

more than one right line onely.

SIMP. There can be but one.

SALV. But yet you underſtand that this onely right line ſhall

again of neceſſity be the ſhorteſt of them all?

again of neceſſity be the ſhorteſt of them all?

SIMP. I know it, and alſo have a demonſtration thereof,

duced by a great Peripatetick Philoſopher, and as I take it, if my

memory do not deceive me, he alledgeth it by way of reprehending

Archimedes, that ſuppoſeth it as known, when it may be

ſtrated.

duced by a great Peripatetick Philoſopher, and as I take it, if my

memory do not deceive me, he alledgeth it by way of reprehending

Archimedes, that ſuppoſeth it as known, when it may be

ſtrated.

SALV. This muſt needs be a great Mathematician, that knew

how to demonſtrate that which Archimedes neither did, nor could

demonſtrate. And if you remember his demonſtration, I would

gladly hear it: for I remember very well, that Archimedes in his

Books, de Sphærà & Cylindro, placeth this Propoſition amongſt the

Poſtulata; and I verily believe that he thought it demonſtrated.

how to demonſtrate that which Archimedes neither did, nor could

demonſtrate. And if you remember his demonſtration, I would

gladly hear it: for I remember very well, that Archimedes in his

Books, de Sphærà & Cylindro, placeth this Propoſition amongſt the

Poſtulata; and I verily believe that he thought it demonſtrated.

SIMP. I think I ſhall remember it, for it is very eaſie and

ſhort.

ſhort.

SALV. The diſgrace of Archimedes, and the honour of this

loſopher ſhall be ſo much the greater.

loſopher ſhall be ſo much the greater.

SIMP. I will deſcribe the Figure of it. Between the points

A and B, [in Fig. 5.] draw the right line A B, and the curve line

A C B, of which we will prove the right to be the ſhorter: and

the proof is this; take a point in the curve-line, which let be C,

and draw two other lines, A C and C B, which two lines together;

are longer than the ſole line A B, for ſo demonſtrateth Euelid.

A and B, [in Fig. 5.] draw the right line A B, and the curve line

A C B, of which we will prove the right to be the ſhorter: and

the proof is this; take a point in the curve-line, which let be C,

and draw two other lines, A C and C B, which two lines together;

are longer than the ſole line A B, for ſo demonſtrateth Euelid.