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# JB/135/082/003

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

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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.

---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

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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.

---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.

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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.

---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.

135

posology

082

ii geometry

003

corollaries

copy/fair copy sheet

3

recto

46200