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p 178
273
Prisms
and
cylinders
are
equal,
whose
bases
and
altitudes
are
reciprocally
proportional.
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p. 179
274
Every
pyramid
that
has
a
triangular
base
is a
third
part
of a
prism
having
the
same
base
and
altitude
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p 180
275
Every
pyramid
is a
third
part
of a
prism,
having
the
same
base
and
altitude.
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p. 181
276
Every
cone
is a
third
part
of a
cylinder,
having
the
same
base
and
altitude.
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p. 182
277
Pyramids
and
cones
upon
equal
bases
are
proportional
to
their
altitudes
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p 183
278
Pyramids
and
cones
of
equal
altitude,
are
proportional
to
their
bases
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p. 183
279
Corollary.
Pyramids
and
cones
are
equal,
whose
bases
and
altitudes
are
reciprocally
proportional.
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p. 184
280
A
hemisphere
is
two
thirds
of its
circumscribing
cylinder.
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p 185
281
Corollary.
A
cone,
globe,
and
cylinder
circumscribing
them,
are
proportional
to
the
numbers
1, 2, 3
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p 185
282
Corollary.
A
globe
is
four
times
a
cone,
whose
base
is
its
great
circle,
and
altitude
its
semi-diameter
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p. 186
283
The
surface
of a
globe
is
four
times
the
area
of
its
great
circle.
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p 187
284
The
surfaces
of
similar
prisms
are
proportional
to
the
squares
of
their
corresponding
lines.
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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
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p. 188
286
If
strait
lines
are
proportional,
their
cubes
will
also
be
proportional
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p. 189
287
Similar
prisms
are
proportional
to
the
cubes
of
their
corresponding
lines.
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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.
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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
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p. 190
290
The
surfaces
of
globes
are
proportional
to
the
squares
of
their
diameters;
being
four
times
the
areas
of
their
great
circles.
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p 190
291
The
magnitudes
of
globes
are
proportional
to
the
cubes
of
their
diameters;
being
two
thirds
of
their
circumscribing
cylinders.
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p 190
292
All
similar
solids
are
as
the
cubes
of
their
corresponding
lines,
because
they
are
composed
of
equal
numbers
of
similar
parts
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292
247
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Identifier: | JB/135/082/003"JB/" can not be assigned to a declared number type with value 135. |
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135 |
posology |
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082 |
ii geometry |
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003 |
corollaries |
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copy/fair copy sheet |
3 |
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recto |
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46200 |
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