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# JB/135/082/002

Completed

p. 151
247

The
three
sides
of a
triangle,
are
in the
same
plain

---page break---

p. 151
248

Corollary.
A
plain
will
pass
through
any
two
strait
lines
which
meet
each
other.

---page break---

p. 152
249

The
common
section
of
two
plains
is a
strait
line.

---page break---

p. 153
250

If a
strait
line
stands
at right
angles
to
two
strait
lines
cutting
one
another,
at the
point
of section,
it will
be perpendicular
to the
plain
in which
those
lines
are
situate.

---page break---

p. 155
251

If a
strait
line
stands
at right
angles
to three
strait
lines
meeting
one
another
in
their
common
section,
those
three
lines
are
in
the
same
plain

---page break---

p 156
252

Two
strait
lines
perpendicular
to
the
same
plain
are
parallels.

---page break---

p 157
253

If
two
strait
lines
be
parallel,
and
one
of
them
stands
at
right
angles
to a
plain,
the
other
will
also
stand
at
right
angles
to
the
same
plain

---page break---

p. 159
254

Lines
which
are
parallel
to the
same
line,
tho'
not
in
the
same
plain
with
it,
are
yet
parallel
to
one
another.

---page break---

p. 160
255

If
two
lines
meeting
each
other,
be
parallel
to
two
lines
meeting
each
other,
tho'
not
in
the
same
plain,
yet
those
lines
will
contain
equal
angles

---page break---

p. 161
256

Plains
to
which
the
same
strait
line
is
perpendicular
are
parallel
to
one
another.

---page break---

p. 162
257

If
two
lines
meeting
each
other,
be
parallel
to
two
other
lines
meeting
each
other,
but
not
in
the
same
plain,
the
plains
which
pass
through
them
will
be
parallel.

---page break---

p. 163
258

If
a
plain
cuts
two
parallel
plains,
their
common
sections
will
be
parallel.

---page break---

p. 164
259

If
two
strait
lines
are
cut
by
parallel
plains,
they
will
be
cut
proportionally.

---page break---

p. 165
260

If a
line
stands
at
right
angles
to
any
plain,
all
the
plains
which
pass
thro'
it
will
be
perpendicular
to
the
same
plain.

---page break---

p 166
261

At
a
given
point
in
a
given
plain,
only
one
perpendicular
can
be
erected
to
that
plain,
on
the
same
side.

---page break---

p. 167
262

If
two
plains
cutting
each
other,
be
perpendicular
to
some
plain
their
common
section
will
also
be
perpendicular
to
that
plain.

---page break---

p. 168
263

If
a
prism
be
cut
by
a
plain
parallel
to
its
base,
the
section
will
be
equal
to
the
base

---page break---

p. 169
264

If
a
cylinder
be
cut
by
a
plain
parallel
to
its
base,
the
section
will
be
a
circle,
equal
to
the
base

---page break---

p. 170
265

If
a
pyramid
be
cut
by
a
plain
parallel
to
its
base,
the
section
will
be
similar
to
the
base

---page break---

p. 171
266

If
a
cone
be
cut
by
a
plain
parallel
to
its
base,
the
section
will
be
a
circle.

---page break---

p. 172
267

If
pyramids
or
cones
of
equal
altitude
standing
upon
the
same
plain,
be
cut
by a
plain
parallel
to
their
bases,
the
sections
and
bases
will
be
proportional.

---page break---

p. 173
268

Prisms
and
cylinders,
of equal
base
and
altitude,
are
equal
to
one
another.

---page break---

p 174
269

Pyramids
and
cones
of
equal
base
and
altitude
are
equal
to
one
another.

---page break---

p 175
270

A
globe
is
equal
to a
pyramid
or
cone,
whose
base
is equal
to
its
surface,
and
altitude
is
equal
to
its
semi-diameter.

---page break---

p 176
271

Prisms
and
cylinders
upon
equal
bases,
are
proportional
to
their
altitudes.

---page break---

p 177
272

Prisms
and
cylinders
of
equal
altitude,
are
proportional
to
their
bases

---page break---

p 178
273

Prisms
and
cylinders
are
equal,
whose
bases
and
altitudes
are
reciprocally
proportional.

Identifier: | JB/135/082/002
"JB/" can not be assigned to a declared number type with value 135.

135

posology

082

ii geometry

002

corollaries

copy/fair copy sheet

3

recto

46200