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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&#x2014;.</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/>
&amp;<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>





Revision as of 09:33, 24 April 2019

Click Here To Edit

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




Identifier: | JB/135/082/003"JB/" can not be assigned to a declared number type with value 135.

Date_1

Marginal Summary Numbering

Box

135

Main Headings

posology

Folio number

082

Info in main headings field

ii geometry

Image

003

Titles

corollaries

Category

copy/fair copy sheet

Number of Pages

3

Recto/Verso

recto

Page Numbering

Penner

Watermarks

Marginals

Paper Producer

Corrections

Paper Produced in Year

Notes public

ID Number

46200

Box Contents

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