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<p>p 178<lb/> | |||
273</p> | |||
<p>Prisms<lb/> | |||
and<lb/> | |||
cylinders<lb/> | |||
are<lb/> | |||
equal,<lb/> | |||
whose<lb/> | |||
bases<lb/> | |||
and<lb/> | |||
altitudes<lb/> | |||
are<lb/> | |||
reciprocally<lb/> | |||
proportional.</p><pb/> | |||
<p>p. 179<lb/> | |||
274</p> | |||
<p>Every<lb/> | |||
pyramid<lb/> | |||
that<lb/> | |||
has<lb/> | |||
a<lb/> | |||
triangular<lb/> | |||
base<lb/> | |||
is a<lb/> | |||
third<lb/> | |||
part<lb/> | |||
of a<lb/> | |||
prism<lb/> | |||
having<lb/> | |||
the<lb/> | |||
same<lb/> | |||
base<lb/> | |||
and<lb/> | |||
altitude</p><pb/> | |||
<p>p 180<lb/> | |||
275</p> | |||
<p>Every<lb/> | |||
pyramid<lb/> | |||
is a<lb/> | |||
third<lb/> | |||
part<lb/> | |||
of a<lb/> | |||
prism,<lb/> | |||
having<lb/> | |||
the<lb/> | |||
same<lb/> | |||
base<lb/> | |||
and<lb/> | |||
altitude.</p><pb/> | |||
<p>p. 181<lb/> | |||
276</p> | |||
<p>Every<lb/> | |||
cone<lb/> | |||
is a<lb/> | |||
third<lb/> | |||
part<lb/> | |||
of a<lb/> | |||
cylinder,<lb/> | |||
having<lb/> | |||
the<lb/> | |||
same<lb/> | |||
base<lb/> | |||
and<lb/> | |||
altitude.</p><pb/> | |||
<p>p. 182<lb/> | |||
277</p> | |||
<p>Pyramids<lb/> | |||
and<lb/> | |||
cones<lb/> | |||
upon<lb/> | |||
equal<lb/> | |||
bases<lb/> | |||
are<lb/> | |||
proportional<lb/> | |||
to<lb/> | |||
their<lb/> | |||
altitudes</p><pb/> | |||
<p>p 183<lb/> | |||
278</p> | |||
<p>Pyramids<lb/> | |||
and<lb/> | |||
cones<lb/> | |||
of<lb/> | |||
equal<lb/> | |||
altitude,<lb/> | |||
are<lb/> | |||
proportional<lb/> | |||
to<lb/> | |||
their<lb/> | |||
bases</p><pb/> | |||
<p>p. 183<lb/> | |||
279</p> | |||
<p>Corollary.<lb/> | |||
Pyramids<lb/> | |||
and<lb/> | |||
cones<lb/> | |||
are<lb/> | |||
equal,<lb/> | |||
whose<lb/> | |||
bases<lb/> | |||
and<lb/> | |||
altitudes<lb/> | |||
are<lb/> | |||
reciprocally<lb/> | |||
proportional.</p><pb/> | |||
<p>p. 184<lb/> | |||
280</p> | |||
<p>A<lb/> | |||
hemisphere<lb/> | |||
is<lb/> | |||
two<lb/> | |||
thirds<lb/> | |||
of its<lb/> | |||
circumscribing<lb/> | |||
cylinder.</p><pb/> | |||
<p>p 185<lb/> | |||
281</p> | |||
<p>Corollary.<lb/> | |||
A<lb/> | |||
cone,<lb/> | |||
globe,<lb/> | |||
and<lb/> | |||
cylinder<lb/> | |||
circumscribing<lb/> | |||
them,<lb/> | |||
are<lb/> | |||
proportional<lb/> | |||
to<lb/> | |||
the<lb/> | |||
numbers<lb/> | |||
1, 2, 3</p><pb/> | |||
<p>p 185<lb/> | |||
282</p> | |||
<p>Corollary.<lb/> | |||
A<lb/> | |||
globe<lb/> | |||
is<lb/> | |||
four<lb/> | |||
times<lb/> | |||
a<lb/> | |||
cone,<lb/> | |||
whose<lb/> | |||
base<lb/> | |||
is<lb/> | |||
its<lb/> | |||
great<lb/> | |||
circle,<lb/> | |||
and<lb/> | |||
altitude<lb/> | |||
its<lb/> | |||
semi-diameter</p><pb/> | |||
<p>p. 186<lb/> | |||
283</p> | |||
<p>The<lb/> | |||
surface<lb/> | |||
of a<lb/> | |||
globe<lb/> | |||
is<lb/> | |||
four<lb/> | |||
times<lb/> | |||
the<lb/> | |||
area<lb/> | |||
of<lb/> | |||
its<lb/> | |||
great<lb/> | |||
circle.</p><pb/> | |||
<p>p 187<lb/> | |||
284</p> | |||
<p>The<lb/> | |||
surfaces<lb/> | |||
of<lb/> | |||
similar<lb/> | |||
prisms<lb/> | |||
are<lb/> | |||
proportional<lb/> | |||
to<lb/> | |||
the<lb/> | |||
squares<lb/> | |||
of<lb/> | |||
their<lb/> | |||
corresponding<lb/> | |||
lines.</p><pb/> | |||
<p>p 187<lb/> | |||
285</p> | |||
<p>Corollary.<lb/> | |||
The<lb/> | |||
surfaces<lb/> | |||
of all<lb/> | |||
similar<lb/> | |||
solids<lb/> | |||
are<lb/> | |||
as<lb/> | |||
the<lb/> | |||
squares<lb/> | |||
of<lb/> | |||
their<lb/> | |||
corresponding<lb/> | |||
lines,<lb/> | |||
being<lb/> | |||
composed<lb/> | |||
of equal<lb/> | |||
numbers,<lb/> | |||
of similar<lb/> | |||
parts</p><pb/> | |||
<p>p. 188<lb/> | |||
286</p> | |||
<p>If<lb/> | |||
<sic>strait</sic><lb/> | |||
lines<lb/> | |||
are<lb/> | |||
proportional,<lb/> | |||
their<lb/> | |||
cubes<lb/> | |||
will<lb/> | |||
also<lb/> | |||
be<lb/> | |||
proportional</p><pb/> | |||
<p>p. 189<lb/> | |||
287</p> | |||
<p>Similar<lb/> | |||
prisms<lb/> | |||
are<lb/> | |||
proportional<lb/> | |||
to<lb/> | |||
the<lb/> | |||
cubes<lb/> | |||
of<lb/> | |||
their<lb/> | |||
corresponding<lb/> | |||
lines.</p><pb/> | |||
<p>p. 190<lb/> | |||
288</p> | |||
<!-- This heading spans columns 288 to 292 --><head>Corollaries—.</head> | |||
<p>Similar<lb/> | |||
cylinders<lb/> | |||
are<lb/> | |||
proportional<lb/> | |||
to<lb/> | |||
the<lb/> | |||
cubes<lb/> | |||
of<lb/> | |||
their<lb/> | |||
axes,<lb/> | |||
or<lb/> | |||
diameters<lb/> | |||
of<lb/> | |||
their<lb/> | |||
bases<lb/> | |||
being<lb/> | |||
of the<lb/> | |||
same<lb/> | |||
magnitude<lb/> | |||
with<lb/> | |||
prisms<lb/> | |||
of equal<lb/> | |||
base<lb/> | |||
and<lb/> | |||
altitude.</p><pb/> | |||
<p>p 190<lb/> | |||
289</p> | |||
<p>Similar<lb/> | |||
pyramids<lb/> | |||
and<lb/> | |||
cones<lb/> | |||
are<lb/> | |||
proportional<lb/> | |||
to<lb/> | |||
the<lb/> | |||
cubes<lb/> | |||
of<lb/> | |||
their<lb/> | |||
corresponding<lb/> | |||
lines,<lb/> | |||
being<lb/> | |||
one<lb/> | |||
third<lb/> | |||
of<lb/> | |||
prisms,<lb/> | |||
or<lb/> | |||
cylinders,<lb/> | |||
that<lb/> | |||
have<lb/> | |||
equal<lb/> | |||
bases<lb/> | |||
&<lb/> | |||
altitudes</p><pb/> | |||
<p>p. 190<lb/> | |||
290</p> | |||
<p>The<lb/> | |||
surfaces<lb/> | |||
of<lb/> | |||
globes<lb/> | |||
are<lb/> | |||
proportional<lb/> | |||
to<lb/> | |||
the<lb/> | |||
squares<lb/> | |||
of<lb/> | |||
their<lb/> | |||
diameters;<lb/> | |||
being<lb/> | |||
four<lb/> | |||
times<lb/> | |||
the<lb/> | |||
areas<lb/> | |||
of<lb/> | |||
their<lb/> | |||
great<lb/> | |||
circles.</p><pb/> | |||
<p>p 190<lb/> | |||
291</p> | |||
<p>The<lb/> | |||
magnitudes<lb/> | |||
of<lb/> | |||
globes<lb/> | |||
are<lb/> | |||
proportional<lb/> | |||
to<lb/> | |||
the<lb/> | |||
cubes<lb/> | |||
of<lb/> | |||
their<lb/> | |||
diameters;<lb/> | |||
being<lb/> | |||
two<lb/> | |||
thirds<lb/> | |||
of<lb/> | |||
their<lb/> | |||
circumscribing<lb/> | |||
cylinders.</p><pb/> | |||
<p>p 190<lb/> | |||
292</p> | |||
<p>All<lb/> | |||
similar<lb/> | |||
solids<lb/> | |||
are<lb/> | |||
as<lb/> | |||
the<lb/> | |||
cubes<lb/> | |||
of<lb/> | |||
their<lb/> | |||
corresponding<lb/> | |||
lines,<lb/> | |||
because<lb/> | |||
they<lb/> | |||
are<lb/> | |||
composed<lb/> | |||
of<lb/> | |||
equal<lb/> | |||
numbers<lb/> | |||
of<lb/> | |||
similar<lb/> | |||
parts</p><pb/> | |||
<p>292<lb/> | |||
247<lb/> | |||
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<hi rend="underline">45</hi></p> | |||
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{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}}{{Completed}} |
p 178
273
Prisms
and
cylinders
are
equal,
whose
bases
and
altitudes
are
reciprocally
proportional.
---page break---
p. 179
274
Every
pyramid
that
has
a
triangular
base
is a
third
part
of a
prism
having
the
same
base
and
altitude
---page break---
p 180
275
Every
pyramid
is a
third
part
of a
prism,
having
the
same
base
and
altitude.
---page break---
p. 181
276
Every
cone
is a
third
part
of a
cylinder,
having
the
same
base
and
altitude.
---page break---
p. 182
277
Pyramids
and
cones
upon
equal
bases
are
proportional
to
their
altitudes
---page break---
p 183
278
Pyramids
and
cones
of
equal
altitude,
are
proportional
to
their
bases
---page break---
p. 183
279
Corollary.
Pyramids
and
cones
are
equal,
whose
bases
and
altitudes
are
reciprocally
proportional.
---page break---
p. 184
280
A
hemisphere
is
two
thirds
of its
circumscribing
cylinder.
---page break---
p 185
281
Corollary.
A
cone,
globe,
and
cylinder
circumscribing
them,
are
proportional
to
the
numbers
1, 2, 3
---page break---
p 185
282
Corollary.
A
globe
is
four
times
a
cone,
whose
base
is
its
great
circle,
and
altitude
its
semi-diameter
---page break---
p. 186
283
The
surface
of a
globe
is
four
times
the
area
of
its
great
circle.
---page break---
p 187
284
The
surfaces
of
similar
prisms
are
proportional
to
the
squares
of
their
corresponding
lines.
---page break---
p 187
285
Corollary.
The
surfaces
of all
similar
solids
are
as
the
squares
of
their
corresponding
lines,
being
composed
of equal
numbers,
of similar
parts
---page break---
p. 188
286
If
strait
lines
are
proportional,
their
cubes
will
also
be
proportional
---page break---
p. 189
287
Similar
prisms
are
proportional
to
the
cubes
of
their
corresponding
lines.
---page break---
p. 190
288
Corollaries—.
Similar
cylinders
are
proportional
to
the
cubes
of
their
axes,
or
diameters
of
their
bases
being
of the
same
magnitude
with
prisms
of equal
base
and
altitude.
---page break---
p 190
289
Similar
pyramids
and
cones
are
proportional
to
the
cubes
of
their
corresponding
lines,
being
one
third
of
prisms,
or
cylinders,
that
have
equal
bases
&
altitudes
---page break---
p. 190
290
The
surfaces
of
globes
are
proportional
to
the
squares
of
their
diameters;
being
four
times
the
areas
of
their
great
circles.
---page break---
p 190
291
The
magnitudes
of
globes
are
proportional
to
the
cubes
of
their
diameters;
being
two
thirds
of
their
circumscribing
cylinders.
---page break---
p 190
292
All
similar
solids
are
as
the
cubes
of
their
corresponding
lines,
because
they
are
composed
of
equal
numbers
of
similar
parts
---page break---
292
247
45
Identifier: | JB/135/082/003"JB/" can not be assigned to a declared number type with value 135. |
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135 |
posology |
||
082 |
ii geometry |
||
003 |
corollaries |
||
copy/fair copy sheet |
3 |
||
recto |
|||
46200 |
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