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

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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.
The truth
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.
The sphere
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.
The definition of
the ſphere.
SALV. So that, if thoſe lines ſhould not be equal, there ſame
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.
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?
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.
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.
SIMP. I think I ſhall remember it, for it is very eaſie and
ſhort.
SALV. The diſgrace of Archimedes, and the honour of this
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.

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