Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 701
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
040/01/1054.jpg
"
pagenum
="
360
"/>
contingent unto the Section in the Point P: Wherefore it alſo
<
lb
/>
maketh Right Angles with the Surface of the Liquid: and that
<
lb
/>
part of the Conoidall Solid which is within the Liquid ſhall move
<
lb
/>
upwards according to the Perpendicular drawn thorow B parallel
<
lb
/>
to R T; and that part which is above the Liquid ſhall move down
<
lb
/>
wards according to that drawn thorow G, parallel to the ſaid R T:
<
lb
/>
And thus it ſhall continue to do ſo long untill that the Conoid be
<
lb
/>
reſtored to uprightneſſe, or to ſtand according to the Perpendicular.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1188
"/>
(a)
<
emph
type
="
italics
"/>
By 10. of the
<
lb
/>
fifth.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1189
"/>
A</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1190
"/>
B</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1191
"/>
(b)
<
emph
type
="
italics
"/>
By 19. of the
<
lb
/>
fifth.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1192
"/>
C</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1193
"/>
(c)
<
emph
type
="
italics
"/>
By 1. of this
<
lb
/>
ſecond Book.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1194
"/>
(d)
<
emph
type
="
italics
"/>
By
<
emph.end
type
="
italics
"/>
6. De Co
<
lb
/>
noilibus &
<
emph
type
="
italics
"/>
S
<
emph.end
type
="
italics
"/>
phæ
<
lb
/>
roidibus
<
emph
type
="
italics
"/>
of
<
emph.end
type
="
italics
"/>
Archi
<
lb
/>
medes.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1195
"/>
D</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1196
"/>
E</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1197
"/>
F</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1198
"/>
(e)
<
emph
type
="
italics
"/>
By 2. of this
<
lb
/>
ſecond Book.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
head
">
<
s
>COMMANDINE.
<
lb
/>
<
arrow.to.target
n
="
marg1199
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1199
"/>
A</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Let therefore R H be equall to the Semi-parameter.]
<
emph
type
="
italics
"/>
So it is to be
<
lb
/>
read, and not R M, as
<
emph.end
type
="
italics
"/>
Tartaglia's
<
emph
type
="
italics
"/>
Tranſlation hath is; which may be made appear from
<
lb
/>
that which followeth.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
marg1200
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1200
"/>
B</
s
>
</
p
>
<
p
type
="
main
">
<
s
>And O H double to H M.]
<
emph
type
="
italics
"/>
In the Tranſlation aforenamed it is falſly render
<
lb
/>
ed,
<
emph.end
type
="
italics
"/>
O N
<
emph
type
="
italics
"/>
double to
<
emph.end
type
="
italics
"/>
R M.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
marg1201
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1201
"/>
C</
s
>
</
p
>
<
p
type
="
main
">
<
s
>And look what proportion the Submerged Portion hath to the whole
<
lb
/>
Portion, the ſame hath the Square of P F unto the Square of N O.]
<
lb
/>
<
emph
type
="
italics
"/>
This place we have reſtored in our Tranſlation, at the requeſt of ſome friends: But it is demon
<
lb
/>
ſtrated by
<
emph.end
type
="
italics
"/>
Archimedes in Libro de Conoidibus & Sphæroidibus, Propo. </
s
>
<
s
>26.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
marg1202
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1202
"/>
D</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Wherefore P F is not leſſe than M O.]
<
emph
type
="
italics
"/>
For by 10 of the fifth it followeth
<
lb
/>
that the Square of P F is not leſſe than the Square of M O: and therefore neither ſhall the
<
lb
/>
Line P F be leße than the Line M O, by 22 of the
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
figure
id
="
id.040.01.1054.1.jpg
"
xlink:href
="
040/01/1054/1.jpg
"
number
="
253
"/>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
marg1203
"/>
<
lb
/>
<
emph
type
="
italics
"/>
ſixth.
<
emph.end
type
="
italics
"/>
<
lb
/>
<
arrow.to.target
n
="
marg1204
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1203
"/>
E</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1204
"/>
(a)
<
emph
type
="
italics
"/>
By 14. of the
<
lb
/>
ſixth.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Nor B P than H O,]
<
emph
type
="
italics
"/>
For as P F is to
<
lb
/>
P B, ſo is M O to H O: and, by Permutation, as
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
marg1205
"/>
<
lb
/>
<
emph
type
="
italics
"/>
P F is to M O, ſo is B P to H O; But P F is not
<
lb
/>
leſſe than M O as hath bin proved; (a) Therefore
<
lb
/>
neither ſhall B P be leſſe than H O.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1205
"/>
F</
s
>
</
p
>
<
p
type
="
main
">
<
s
>If therefore a Right Line be drawn
<
lb
/>
from H at Right Angles unto N O, it
<
lb
/>
ſhall meet with B P, and ſhall fall be
<
lb
/>
twixt B and P.]
<
emph
type
="
italics
"/>
This Place was corrupt in the
<
lb
/>
Tranſlation of
<
emph.end
type
="
italics
"/>
Tartaglia
<
emph
type
="
italics
"/>
: But it is thus demonstra
<
lb
/>
ted. </
s
>
<
s
>In regard that P F is not leſſe than O M, nor P B than O H, if we ſuppoſe P F equall to
<
lb
/>
O M, P B ſhall be likewiſe equall to O H: Wherefore the Line drawn thorow O, parallel to A L
<
lb
/>
ſhall fall without the Section, by 17 of the firſt of our Treatiſe of Conicks; And in regard that
<
lb
/>
B P prolonged doth meet it beneath P; Therefore the Perpendicular drawn thorow H doth
<
lb
/>
alſo meet with the ſame beneath B, and it doth of neceſſity fall betwixt B and P: But the
<
lb
/>
ſame is much more to follow, if we ſuppoſe P F to be greater than O M.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>