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<p>p 84<lb/> | |||
144</p> | |||
<p>The<lb/> | |||
opposite<lb/> | |||
angles<lb/> | |||
of<lb/> | |||
any<lb/> | |||
quadrangle<lb/> | |||
inscribed<lb/> | |||
in<lb/> | |||
a circle,<lb/> | |||
are<lb/> | |||
equal<lb/> | |||
to two<lb/> | |||
right<lb/> | |||
angles</p><pb/> | |||
<p>p 85<lb/> | |||
145</p> | |||
<p>Corollary.<lb/> | |||
If any<lb/> | |||
side of<lb/> | |||
a quadrangle<lb/> | |||
inscribed<lb/> | |||
in a<lb/> | |||
circle<lb/> | |||
is produced<lb/> | |||
the<lb/> | |||
outward<lb/> | |||
angle<lb/> | |||
will<lb/> | |||
be equal<lb/> | |||
to the<lb/> | |||
inward<lb/> | |||
and<lb/> | |||
opposite<lb/> | |||
angle</p><pb/> | |||
<p>p 85<lb/> | |||
146</p> | |||
<p>Corollary.<lb/> | |||
If two<lb/> | |||
opposite<lb/> | |||
angles<lb/> | |||
of a<lb/> | |||
quadrangle<lb/> | |||
taken<lb/> | |||
together<lb/> | |||
be equal<lb/> | |||
to two<lb/> | |||
right<lb/> | |||
angles<lb/> | |||
a circle<lb/> | |||
may<lb/> | |||
be<lb/> | |||
circumscribed<lb/> | |||
about the figure</p><pb/> | |||
<p>p 86<lb/> | |||
147</p> | |||
<p>Similar<lb/> | |||
segments<lb/> | |||
of circles<lb/> | |||
upon<lb/> | |||
equal<lb/> | |||
bases<lb/> | |||
are<lb/> | |||
equal<lb/> | |||
to one<lb/> | |||
another</p><pb/> | |||
<p>p 87<lb/> | |||
148</p> | |||
<p>In<lb/> | |||
equal<lb/> | |||
circles,<lb/> | |||
equal<lb/> | |||
angles<lb/> | |||
either<lb/> | |||
at the<lb/> | |||
<sic>centers</sic><lb/> | |||
or circumferences,<lb/> | |||
intercept<lb/> | |||
equal<lb/> | |||
arches.</p><pb/> | |||
<p>p 87<lb/> | |||
149</p> | |||
<p>Corollary.<lb/> | |||
In<lb/> | |||
equal<lb/> | |||
circles<lb/> | |||
the<lb/> | |||
sectors<lb/> | |||
of<lb/> | |||
equal<lb/> | |||
angles<lb/> | |||
are<lb/> | |||
equal<lb/> | |||
to one<lb/> | |||
another.</p><pb/> | |||
<p>p 88<lb/> | |||
150</p> | |||
<p>In equal<lb/> | |||
circles,<lb/> | |||
angles<lb/> | |||
standing<lb/> | |||
upon<lb/> | |||
equal<lb/> | |||
arches<lb/> | |||
are<lb/> | |||
equal<lb/> | |||
either<lb/> | |||
at the<lb/> | |||
<sic>centers</sic><lb/> | |||
or<lb/> | |||
circumferences</p><pb/> | |||
<p>p 89<lb/> | |||
151</p> | |||
<p>In<lb/> | |||
equal<lb/> | |||
circles,<lb/> | |||
equal<lb/> | |||
<sic>strait</sic><lb/> | |||
lines<lb/> | |||
cut<lb/> | |||
off<lb/> | |||
equal<lb/> | |||
parts<lb/> | |||
of the<lb/> | |||
circumferences<lb/> | |||
the<lb/> | |||
lesser<lb/> | |||
arch<lb/> | |||
equal<lb/> | |||
to the<lb/> | |||
lesser,<lb/> | |||
and<lb/> | |||
the<lb/> | |||
greater<lb/> | |||
arch<lb/> | |||
equal<lb/> | |||
to the<lb/> | |||
greater.</p><pb/> | |||
<p>p 90<lb/> | |||
152</p> | |||
<p>In equal<lb/> | |||
circles<lb/> | |||
equal<lb/> | |||
arches<lb/> | |||
are<lb/> | |||
subtended<lb/> | |||
by<lb/> | |||
equal<lb/> | |||
<sic>strait</sic><lb/> | |||
lines</p><pb/> | |||
<p>p 91<lb/> | |||
153</p> | |||
<p>An<lb/> | |||
angle<lb/> | |||
in a<lb/> | |||
semicircle<lb/> | |||
is a<lb/> | |||
right<lb/> | |||
angle</p><pb/> | |||
<p>p 92<lb/> | |||
154</p> | |||
<p>An<lb/> | |||
angle<lb/> | |||
in<lb/> | |||
the<lb/> | |||
segment<lb/> | |||
of a<lb/> | |||
circle<lb/> | |||
differs<lb/> | |||
from<lb/> | |||
a right<lb/> | |||
one,<lb/> | |||
by<lb/> | |||
the<lb/> | |||
angle<lb/> | |||
contained<lb/> | |||
between<lb/> | |||
the<lb/> | |||
base<lb/> | |||
of the<lb/> | |||
segment<lb/> | |||
and<lb/> | |||
a<lb/> | |||
diameter<lb/> | |||
drawn<lb/> | |||
from<lb/> | |||
its<lb/> | |||
extremity.</p> | |||
<p>Remark.<lb/> | |||
An<lb/> | |||
angle<lb/> | |||
in<lb/> | |||
the<lb/> | |||
greater<lb/> | |||
segment<lb/> | |||
of a<lb/> | |||
circle<lb/> | |||
is acute,<lb/> | |||
but<lb/> | |||
in<lb/> | |||
the<lb/> | |||
lesser<lb/> | |||
it is<lb/> | |||
obtuse.</p><pb/> | |||
<p>p 93<lb/> | |||
155</p> | |||
<p>The<lb/> | |||
angles<lb/> | |||
made<lb/> | |||
by a<lb/> | |||
tangent<lb/> | |||
and<lb/> | |||
a<lb/> | |||
line<lb/> | |||
drawn<lb/> | |||
from<lb/> | |||
the<lb/> | |||
point<lb/> | |||
of contact<lb/> | |||
cutting<lb/> | |||
the<lb/> | |||
circle,<lb/> | |||
are<lb/> | |||
equal<lb/> | |||
to the<lb/> | |||
angles<lb/> | |||
contained<lb/> | |||
in<lb/> | |||
the<lb/> | |||
opposite<lb/> | |||
segments<lb/> | |||
of the<lb/> | |||
circle.</p> | |||
p 84
144
The
opposite
angles
of
any
quadrangle
inscribed
in
a circle,
are
equal
to two
right
angles
---page break---
p 85
145
Corollary.
If any
side of
a quadrangle
inscribed
in a
circle
is produced
the
outward
angle
will
be equal
to the
inward
and
opposite
angle
---page break---
p 85
146
Corollary.
If two
opposite
angles
of a
quadrangle
taken
together
be equal
to two
right
angles
a circle
may
be
circumscribed
about the figure
---page break---
p 86
147
Similar
segments
of circles
upon
equal
bases
are
equal
to one
another
---page break---
p 87
148
In
equal
circles,
equal
angles
either
at the
centers
or circumferences,
intercept
equal
arches.
---page break---
p 87
149
Corollary.
In
equal
circles
the
sectors
of
equal
angles
are
equal
to one
another.
---page break---
p 88
150
In equal
circles,
angles
standing
upon
equal
arches
are
equal
either
at the
centers
or
circumferences
---page break---
p 89
151
In
equal
circles,
equal
strait
lines
cut
off
equal
parts
of the
circumferences
the
lesser
arch
equal
to the
lesser,
and
the
greater
arch
equal
to the
greater.
---page break---
p 90
152
In equal
circles
equal
arches
are
subtended
by
equal
strait
lines
---page break---
p 91
153
An
angle
in a
semicircle
is a
right
angle
---page break---
p 92
154
An
angle
in
the
segment
of a
circle
differs
from
a right
one,
by
the
angle
contained
between
the
base
of the
segment
and
a
diameter
drawn
from
its
extremity.
Remark.
An
angle
in
the
greater
segment
of a
circle
is acute,
but
in
the
lesser
it is
obtuse.
---page break---
p 93
155
The
angles
made
by a
tangent
and
a
line
drawn
from
the
point
of contact
cutting
the
circle,
are
equal
to the
angles
contained
in
the
opposite
segments
of the
circle.
|
Identifier: | JB/135/081/003"JB/" can not be assigned to a declared number type with value 135. |
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|---|---|---|---|
|
135 |
posology |
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|
081 |
geometry i |
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|
003 |
no. 125 p. 67 |
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copy/fair copy sheet |
3 |
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|
recto |
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46199 |
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