Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 570
571 - 600
601 - 630
631 - 660
661 - 690
691 - 701
>
Scan
Original
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 570
571 - 600
601 - 630
631 - 660
661 - 690
691 - 701
>
page
|<
<
of 701
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
040/01/124.jpg
"
pagenum
="
106
"/>
ſwer, that of infinite one part is not greater than another, ſince
<
lb
/>
<
arrow.to.target
n
="
marg273
"/>
<
lb
/>
both are infinite; nor can it be ſaid, that of the infinite number,
<
lb
/>
an hundred thouſand is a greater part than two, though that be
<
lb
/>
fifty thouſand times greater than this; and if to the moving of
<
lb
/>
the Univerſe there be required a finite power, though very great
<
lb
/>
in compariſon of that which ſufficeth to move the Earth onely;
<
lb
/>
yet is there not implied therein a greater part of the infinite power,
<
lb
/>
nor is that part leſſe infinite which remaineth unimploy'd. </
s
>
<
s
>So that
<
lb
/>
to apply unto a particular effect, a little more, or a little leſſe
<
lb
/>
power, importeth nothing; beſides that the operation of ſuch
<
lb
/>
vertue, hath not for its bound or end the Diurnal Motion onely;
<
lb
/>
but there are ſeveral other motions in the World, which we
<
lb
/>
know of, and many others there may be, that are to us unknown.
<
lb
/>
</
s
>
<
s
>Therefore if we reſpect the Moveables, and granting it as out of
<
lb
/>
queſtion, that it is a ſhorter and eaſier way to move the Earth,
<
lb
/>
than the Univerſe; and moreover, having an eye to the ſo many
<
lb
/>
other abreviations, and facilities that onely this way are to be
<
lb
/>
tained, an infallible Maxime of
<
emph
type
="
italics
"/>
Ariſtotle,
<
emph.end
type
="
italics
"/>
which he teacheth us,
<
lb
/>
that,
<
emph
type
="
italics
"/>
fruſtra fit per plura, quod poteſt fieri per pauciora,
<
emph.end
type
="
italics
"/>
<
lb
/>
dereth it more probable that the Diurnal Motion belongs to the
<
lb
/>
Earth alone, than to the Univerſe, the Earth ſubducted.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg273
"/>
<
emph
type
="
italics
"/>
Of infinity one
<
lb
/>
part is no bigger
<
lb
/>
than auother,
<
lb
/>
though they are
<
lb
/>
comparatively
<
lb
/>
equal.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SIMPL. </
s
>
<
s
>In reciting that Axiom, you have omitted a ſmall
<
lb
/>
clauſe, which importeth as much as all the reſt, eſpecially in our
<
lb
/>
caſe, that is to ſay, the words
<
emph
type
="
italics
"/>
æquè bene.
<
emph.end
type
="
italics
"/>
It is requiſite therefore
<
lb
/>
to examine whether this
<
emph
type
="
italics
"/>
Hypotheſis
<
emph.end
type
="
italics
"/>
doth
<
emph
type
="
italics
"/>
equally well
<
emph.end
type
="
italics
"/>
ſatisfie in all
<
lb
/>
particulars, as the other.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>The knowledg whether both theſe poſitions do
<
emph
type
="
italics
"/>
æquè
<
lb
/>
bene,
<
emph.end
type
="
italics
"/>
ſatisfie, may be comprehended from the particular
<
lb
/>
nation of the appearances which they are to ſatisfie; for hitherto
<
lb
/>
we have diſcourſed, and will continue to argue
<
emph
type
="
italics
"/>
ex hypotheſi,
<
emph.end
type
="
italics
"/>
<
lb
/>
namely, ſuppoſing, that as to the ſatisfaction of the appearances,
<
lb
/>
<
arrow.to.target
n
="
marg274
"/>
<
lb
/>
both the aſſumptions are equally accomodated. </
s
>
<
s
>As to the clauſe
<
lb
/>
which you ſay was omitted by me, I have more reaſon to ſuſpect
<
lb
/>
that it was ſuperfluouſly inſerted by you. </
s
>
<
s
>For the expreſſion
<
emph
type
="
italics
"/>
æquè
<
lb
/>
bene,
<
emph.end
type
="
italics
"/>
is a relative that neceſſarily requireth two terms at leaſt,
<
lb
/>
for a thing cannot have relation to its ſelf, nor do we ſay,
<
emph
type
="
italics
"/>
v. </
s
>
<
s
>gr.
<
emph.end
type
="
italics
"/>
<
lb
/>
reſt to be
<
emph
type
="
italics
"/>
equally good,
<
emph.end
type
="
italics
"/>
as reſt. </
s
>
<
s
>And becauſe, when we ſay,
<
emph
type
="
italics
"/>
that
<
lb
/>
is done in vain by many means, which may be done with fewer,
<
emph.end
type
="
italics
"/>
<
lb
/>
we mean, that that which is to be done, ought to be the ſame
<
lb
/>
thing, not two different ones; and becauſe the ſame thing
<
lb
/>
not be ſaid to be done as well as its ſelf; therefore, the addition
<
lb
/>
of the Phraſe
<
emph
type
="
italics
"/>
æquè bene
<
emph.end
type
="
italics
"/>
is ſuperfluous, and a relation, that hath
<
lb
/>
but one term onely.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg274
"/>
<
emph
type
="
italics
"/>
In the Axiome
<
emph.end
type
="
italics
"/>
<
lb
/>
Fruſtra fit per
<
lb
/>
ra, &c.
<
emph
type
="
italics
"/>
the
<
lb
/>
tion of
<
emph.end
type
="
italics
"/>
æque benè,
<
lb
/>
<
emph
type
="
italics
"/>
is ſuperfluous.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SAGR. </
s
>
<
s
>Unleſſe you will have the ſame befal us, as did
<
lb
/>
day, let us return to our matter in hand; and let
<
emph
type
="
italics
"/>
Simplicius
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>