Archimedes
,
Natation of bodies
,
1662
Text
Text Image
XML
Document information
None
Concordance
Figures
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 68
>
Scan
Original
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
<
1 - 30
31 - 60
61 - 68
>
page
|<
<
of 68
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
073/01/028.jpg
"
pagenum
="
357
"/>
<
figure
id
="
id.073.01.028.1.jpg
"
xlink:href
="
073/01/028/1.jpg
"
number
="
24
"/>
<
lb
/>
<
emph
type
="
italics
"/>
Angle K H M: Therefore
<
emph.end
type
="
italics
"/>
(f) O G
<
emph
type
="
italics
"/>
and H N are parallel,
<
emph.end
type
="
italics
"/>
<
lb
/>
<
arrow.to.target
n
="
marg1184
"/>
<
lb
/>
<
emph
type
="
italics
"/>
and the
<
emph.end
type
="
italics
"/>
(g)
<
emph
type
="
italics
"/>
Angle H N F equall to the Angle O G F; for
<
lb
/>
that G O being Perpendicular to E F, H N ſhall alſo be per-
<
emph.end
type
="
italics
"/>
<
lb
/>
<
arrow.to.target
n
="
marg1185
"/>
<
lb
/>
<
emph
type
="
italics
"/>
pandicnlar to the ſame: Which was to be demon ſtrated.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1179
"/>
(a)
<
emph
type
="
italics
"/>
By Cor. </
s
>
<
s
>of 8. of
<
lb
/>
6. of
<
emph.end
type
="
italics
"/>
Euclide.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1180
"/>
(b)
<
emph
type
="
italics
"/>
By 17. of the
<
emph.end
type
="
italics
"/>
<
lb
/>
6.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1181
"/>
(c)
<
emph
type
="
italics
"/>
By 14. of the
<
emph.end
type
="
italics
"/>
<
lb
/>
6.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1182
"/>
(d)
<
emph
type
="
italics
"/>
By 33. of the
<
emph.end
type
="
italics
"/>
<
lb
/>
1.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1183
"/>
(e)
<
emph
type
="
italics
"/>
By 4. of the
<
emph.end
type
="
italics
"/>
1.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1184
"/>
(f)
<
emph
type
="
italics
"/>
By 28. of the
<
emph.end
type
="
italics
"/>
<
lb
/>
1.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1185
"/>
(g)
<
emph
type
="
italics
"/>
By 29. of th
<
emph.end
type
="
italics
"/>
<
lb
/>
1</
s
>
</
p
>
<
p
type
="
main
">
<
s
>And the part which is within the Liquid
<
lb
/>
<
arrow.to.target
n
="
marg1186
"/>
<
lb
/>
doth move upwards according to the Per
<
lb
/>
pendicular that is drawn thorow B parallel
<
lb
/>
to R T.]
<
emph
type
="
italics
"/>
The reaſon why this moveth upwards, and that
<
lb
/>
other downwards, along the Perpendicular Line, hath been ſhewn above in the 8 of the firſt
<
lb
/>
Book of this; ſo that we have judged it needleſſe to repeat it either in this, or in the reſt
<
lb
/>
that follow.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1186
"/>
G</
s
>
</
p
>
<
p
type
="
head
">
<
s
>THE TRANSLATOR.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
In the
<
emph.end
type
="
italics
"/>
Antient
<
emph
type
="
italics
"/>
Parabola (namely that aſſumed in a Rightangled
<
lb
/>
Cone) the Line
<
emph.end
type
="
italics
"/>
juxta quam Poſſunt quæ in Sectione ordinatim du
<
lb
/>
cuntur
<
emph
type
="
italics
"/>
(which I, following
<
emph.end
type
="
italics
"/>
Mydorgius,
<
emph
type
="
italics
"/>
do call the
<
emph.end
type
="
italics
"/>
Parameter
<
emph
type
="
italics
"/>
) is
<
emph.end
type
="
italics
"/>
(a)
<
lb
/>
<
arrow.to.target
n
="
marg1187
"/>
<
lb
/>
<
emph
type
="
italics
"/>
double to that
<
emph.end
type
="
italics
"/>
quæ ducta eſt à Vertice Sectionis uſque ad Axem,
<
emph
type
="
italics
"/>
or in
<
emph.end
type
="
italics
"/>
<
lb
/>
Archimedes
<
emph
type
="
italics
"/>
phraſe,
<
emph.end
type
="
italics
"/>
<
foreign
lang
="
grc
">τᾱς υσ́χρι τοῡ ἄξον<34>;</
foreign
>
<
emph
type
="
italics
"/>
which I for that cauſe, and
<
lb
/>
for want of a better word, name the
<
emph.end
type
="
italics
"/>
Semiparameter:
<
emph
type
="
italics
"/>
but in
<
emph.end
type
="
italics
"/>
Modern
<
lb
/>
<
emph
type
="
italics
"/>
Parabola's it is greater or leſſer then double. </
s
>
<
s
>Now that throughout this
<
lb
/>
Book
<
emph.end
type
="
italics
"/>
Archimedes
<
emph
type
="
italics
"/>
ſpeaketh of the Parabola in a Rectangled Cone, is mani
<
lb
/>
feſt both by the firſt words of each Propoſition, & by this that no Parabola
<
lb
/>
hath its Parameter double to the Line
<
emph.end
type
="
italics
"/>
quæ eſt a Sectione ad Axem,
<
emph
type
="
italics
"/>
ſave
<
lb
/>
that which is taken in a Rightangled Cone. </
s
>
<
s
>And in any other Parabola, for
<
lb
/>
the Line
<
emph.end
type
="
italics
"/>
<
foreign
lang
="
grc
">τᾱς μσ́χριτοῡ ἄεον<34></
foreign
>
<
emph
type
="
italics
"/>
or
<
emph.end
type
="
italics
"/>
quæ uſque ad Axem
<
emph
type
="
italics
"/>
to uſurpe the Word
<
emph.end
type
="
italics
"/>
Se
<
lb
/>
miparameter
<
emph
type
="
italics
"/>
would be neither proper nor true: but in this caſe it may paſs
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1187
"/>
(a) Rîvalt.
<
emph
type
="
italics
"/>
in
<
emph.end
type
="
italics
"/>
Ar
<
lb
/>
chimed.
<
emph
type
="
italics
"/>
de Cunoid
<
lb
/>
& Sphæroid.
<
emph.end
type
="
italics
"/>
Prop.
<
lb
/>
</
s
>
<
s
>3. Lem. </
s
>
<
s
>1.</
s
>
</
p
>
<
p
type
="
head
">
<
s
>PROP. III. THEOR. III.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
The Right Portion of a Rightangled Conoid, when it
<
lb
/>
ſhall have its Axis leſſe than ſeſquialter of the Se
<
lb
/>
mi-parameter, the Axis having any what ever pro
<
lb
/>
portion to the Liquid in Gravity, being demitted into
<
lb
/>
the Liquid ſo as that its Baſe be wholly within the
<
lb
/>
ſaid Liquid, and being ſet inclining, it ſhall not re
<
lb
/>
main inclined, but ſhall be ſo reſtored, as that its Ax
<
lb
/>
is do ſtand upright, or according to the Perpendicular.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Let any Portion be demitted into the Liquid, as was ſaid; and
<
lb
/>
let its Baſe be in the
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
iquid;
<
lb
/>
<
figure
id
="
id.073.01.028.2.jpg
"
xlink:href
="
073/01/028/2.jpg
"
number
="
25
"/>
<
lb
/>
and let it be cut thorow the
<
lb
/>
Axis, by a Plain erect upon the Sur
<
lb
/>
face of the Liquid, and let the Se
<
lb
/>
ction be A P O
<
emph
type
="
italics
"/>
L,
<
emph.end
type
="
italics
"/>
the Section of a
<
lb
/>
Right angled Cone: and let the Axis
<
lb
/>
of the Portion and Diameter of the </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>