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< | <p><!-- Pencil heading -->N<hi rend="superscript">o</hi> 125. p.67</p> | ||
< | <p>p.67<lb/> | ||
125</ | 125</p> | ||
<lb/> | |||
<p>A<lb/> | <p>A<lb/> | ||
strait <lb/> | strait <lb/> | ||
Line 19: | Line 19: | ||
circle <lb/> | circle <lb/> | ||
will <lb/> | will <lb/> | ||
fall | fall <lb/> | ||
<lb/> | |||
with <lb/> | with <lb/> | ||
in the <lb/> | in the <lb/> | ||
circle</p | circle</p> | ||
< | <pb/> | ||
126</ | <p>p.68 <lb/> | ||
<p>A <lb/> | 126</p> | ||
<p>A <lb/> | |||
line <lb/> | line <lb/> | ||
drawn <lb/> | drawn <lb/> | ||
Line 49: | Line 49: | ||
at <lb/> | at <lb/> | ||
right <lb/> | right <lb/> | ||
angles.</p | angles.</p> | ||
< | <pb/> | ||
127</ | <p>p 69<lb/> | ||
127</p> | |||
<lb/> | |||
<p>A<lb/> | <p>A<lb/> | ||
line<lb/> | line<lb/> | ||
Line 73: | Line 75: | ||
divide<lb/> | divide<lb/> | ||
it<lb/> | it<lb/> | ||
equally</p | equally</p> | ||
<pb/> | |||
<p>P.70<lb/> | |||
128</p> | |||
<p>If<lb/> | <p>If<lb/> | ||
a <lb/> | a <lb/> | ||
Line 102: | Line 104: | ||
of<lb/> | of<lb/> | ||
the <lb/> | the <lb/> | ||
circle.</p | circle.</p> | ||
< | <pb/> | ||
129</ | <p>p 71<lb/> | ||
129</p> | |||
<p>If <lb/> | |||
from <lb/> | |||
a <lb/> | |||
certain <lb/> | |||
point<lb/> | |||
within <lb/> | |||
a <lb/> | |||
circle <lb/> | |||
three <lb/> | |||
equal <lb/> | |||
strait <lb/> | |||
lines <lb/> | |||
be <lb/> | |||
drawn <lb/> | |||
to the <lb/> | |||
circumference <lb/> | |||
that <lb/> | |||
point <lb/> | |||
is the <lb/> | |||
center <lb/> | |||
of the <lb/> | |||
circle.</p> | |||
< | <pb/> | ||
<p>p 72<lb/> | |||
130</p> | |||
<p>In <lb/> | |||
a <lb/> | |||
circle <lb/> | |||
equal <lb/> | |||
strait <lb/> | |||
lines <lb/> | |||
terminated <lb/> | |||
by <lb/> | |||
the <lb/> | |||
circumference <lb/> | |||
are <lb/> | |||
equally <lb/> | |||
distant <lb/> | |||
from <lb/> | |||
the <lb/> | |||
center</p> | |||
< | <pb/> | ||
<p>p 73<lb/> | |||
131</p> | |||
<p>In <lb/> | |||
a <lb/> | |||
circle <lb/> | |||
strait <lb/> | |||
lines <lb/> | |||
equally <lb/> | |||
distant <lb/> | |||
from <lb/> | |||
the <lb/> | |||
centre, <lb/> | |||
& <lb/> | |||
terminated <lb/> | |||
by <lb/> | |||
the <lb/> | |||
circumference,<lb/> | |||
are <lb/> | |||
equal <lb/> | |||
to one <lb/> | |||
another.</p><p>p 74<lb/> | |||
132</p> | |||
<p>In <lb/> | |||
circles <lb/> | |||
the <lb/> | |||
greatest <lb/> | |||
line <lb/> | |||
is a <lb/> | |||
diameter, <lb/> | |||
and of <lb/> | |||
other <lb/> | |||
lines <lb/> | |||
the <lb/> | |||
nearer <lb/> | |||
to <lb/> | |||
the <lb/> | |||
centre <lb/> | |||
is <lb/> | |||
the <lb/> | |||
greater,</p> | |||
<p> | <pb/> | ||
<p>p 75<lb/> | |||
133</p> | |||
<p>Of <lb/> | |||
strait <lb/> | |||
lines <lb/> | |||
drawn <lb/> | |||
from <lb/> | |||
the <lb/> | |||
same <lb/> | |||
point <lb/> | |||
to the <lb/> | |||
circumference <lb/> | |||
of a <lb/> | |||
circle, <lb/> | |||
the <lb/> | |||
greatest <lb/> | |||
is <lb/> | |||
that <lb/> | |||
passing <lb/> | |||
through <lb/> | |||
its <lb/> | |||
centre, <lb/> | |||
&<lb/> | |||
the <lb/> | |||
least <lb/> | |||
falls <lb/> | |||
in the <lb/> | |||
opposite <lb/> | |||
point <lb/to the <lb/> | |||
greatest.</p> | |||
< | <pb/> | ||
<p>p76 <lb/> | |||
134</p> | |||
<p>Only <lb/> | |||
two <lb/> | |||
equal <lb/> | |||
lines <lb/> | |||
can <lb/> | |||
be <lb/> | |||
drawn <lb/> | |||
to the <lb/> | |||
circumference <lb/> | |||
of a <lb/> | |||
circle, <lb/> | |||
from <lb/> | |||
any <lb/> | |||
point <lb/> | |||
which <lb/> | |||
is not <lb/> | |||
its <lb/> | |||
<sic>center</sic></p> | |||
< | <pb/> | ||
<p>p76<lb/> | |||
135</p> | |||
<p>Corollary. <lb/> | |||
One <lb/> | |||
circle <lb/> | |||
can <lb/> | |||
cut <lb/> | |||
another <lb/> | |||
in <lb/> | |||
two <lb/> | |||
points <lb/> | |||
only</p> | |||
< | <pb/> | ||
<p>p77 <lb/> | |||
136</p> | |||
<p>If <lb/> | |||
two <lb/> | |||
circles <lb/> | |||
touch <lb/> | |||
one <lb/> | |||
another, <lb/> | |||
a <lb/> | |||
<sic>strait</sic> <lb/> | |||
line <lb/> | |||
joining <lb/> | |||
their <lb/> | |||
<sic>centers</sic> <lb/> | |||
will <lb/> | |||
fall <lb/> | |||
in the <lb/> | |||
point <lb/> | |||
of <lb/> | |||
contact</p> | |||
<p> | <pb/> | ||
<p>p 78<lb/> | |||
136</p> | |||
<p>Case <lb/> | |||
2.<lb/> | |||
When <lb/> | |||
the <lb/> | |||
circles <lb/> | |||
touch <lb/> | |||
inwardly <lb/> | |||
a <lb/> | |||
<sic>strait</sic> <lb/> | |||
line <lb/> | |||
joining <lb/> | |||
their <lb/> | |||
<sic>centers</sic> <lb/> | |||
will <lb/> | |||
fall <lb/> | |||
in the <lb/> | |||
point <lb/> | |||
of <lb/> | |||
contact</p> | |||
< | <pb/> | ||
<p>p78 <lb/> | |||
137</p> | |||
<p>Corollary. <lb/> | |||
One <lb/> | |||
circle <lb/> | |||
can <lb/> | |||
touch <lb/> | |||
another <lb/> | |||
in <lb/> | |||
one <lb/> | |||
point <lb/> | |||
only</p> | |||
<pb/> | |||
<p>p79 <lb/> | |||
138</p> | |||
<p>A <lb/> | |||
<sic>strait</sic> <lb/> | |||
line <lb/> | |||
drawn <lb/> | |||
at <lb/> | |||
right <lb/> | |||
angles <lb/> | |||
to the <lb/> | |||
extremity <lb/> | |||
of a <lb/> | |||
diameter, <lb/> | |||
is a <lb/> | |||
tangent <lb/> | |||
to the <lb/> | |||
circle.</p> | |||
< | <pb/> | ||
<p>p79 <lb/> | |||
139</p> | |||
<p>Corollary <lb/> | |||
A <lb/> | |||
<sic>strait</sic> <lb/> | |||
line <lb/> | |||
can <lb/> | |||
touch <lb/> | |||
a <lb/> | |||
circle <lb/> | |||
in <lb/> | |||
one <lb/> | |||
point <lb/> | |||
only</p> | |||
<p> | <pb/> | ||
< | <p>p 80 <lb/> | ||
140</p> | |||
<p>A <lb/> | |||
line <lb/> | |||
drawn <lb/> | |||
from <lb/> | |||
the <lb/> | |||
centre <lb/> | |||
of <lb/> | |||
a <lb/> | |||
circle <lb/> | |||
to the <lb/> | |||
point <lb/> | |||
of <lb/> | |||
contact <lb/> | |||
will <lb/> | |||
be <lb/> | |||
perpendicular <lb/> | |||
to the <lb/> | |||
tangent</p> | |||
< | <pb/> | ||
<p>p81 <lb/> | |||
141</p> | |||
<p>A <lb/> | |||
line <lb/> | |||
drawn <lb/> | |||
at <lb/> | |||
right <lb/> | |||
angles <lb/> | |||
to a <lb/> | |||
tangent <lb/> | |||
at <lb/> | |||
the <lb/> | |||
point <lb/> | |||
of <lb/> | |||
contact <lb/> | |||
will <lb/> | |||
pass <lb/> | |||
thro' <lb/> | |||
the <lb/> | |||
centre <lb/> | |||
of <lb/> | |||
the <lb/> | |||
circle</p> | |||
< | <pb/> | ||
<p>p82 <lb/> | |||
142</p> | |||
<p>An <lb/> | |||
angle <lb/> | |||
at the <lb/> | |||
centre <lb/> | |||
of <lb/> | |||
a <lb/> | |||
circle <lb/> | |||
is <lb/> | |||
double <lb/> | |||
to <lb/> | |||
an <lb/> | |||
angle <lb/> | |||
at the <lb/> | |||
circumference <lb/> | |||
standing <lb/> | |||
upon <lb/> | |||
the <lb/> | |||
same <lb/> | |||
arch</p> | |||
< | <pb/> | ||
<p>p. 83<lb/> | |||
143</p> | |||
<p>All <lb/> | |||
angles <lb/> | |||
in <lb/> | |||
the <lb/> | |||
same <lb/> | |||
segment <lb/> | |||
of a <lb/> | |||
circle <lb/> | |||
are <lb/> | |||
equal <lb/> | |||
to <lb/> | |||
one <lb/> | |||
another</p> | |||
< | <pb/> | ||
<p>p. 84<lb/> | |||
144</p> | |||
<p>The <lb/> | |||
opposite <lb/> | |||
angles <lb/> | |||
of <lb/> | |||
any <lb/> | |||
quadrangle <lb/> | |||
<sic>inserited</sic> <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>Corrolarly <lb/> | |||
If any <lb/> | |||
side of <lb/> | |||
a quadrangle <lb/> | |||
<sic>inserited</sic> <lb/> | |||
in <lb/> | |||
a circle <lb/> | |||
is produced <lb/> | |||
the <lb/> | |||
outward <lb/> | |||
angles <lb/> | |||
will <lb/> | |||
be equal <lb/> | |||
to the <lb/> | |||
inward <lb/> | |||
and <lb/> | |||
opposite <lb/> | |||
angles.</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 <lb/> | |||
the <lb/> | |||
figure.</p> | |||
<!-- DO NOT EDIT BELOW THIS LINE --> | <!-- DO NOT EDIT BELOW THIS LINE --> | ||
{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}} |
No 125. p.67
p.67
125
A
strait
line
that
joins
any
two
points
in the
circumference
of a
circle
will
fall
with
in the
circle
---page break---
p.68
126
A
line
drawn
from
the
centre
of
a circle,
to
the
middle
of a
line
terminated
by the
circumference
will
meet
the
same
at
right
angles.
---page break---
p 69
127
A
line
drawn
from
the
centre
of
a circle
at
right
angles
to a
line
terminated
by
the
circumference
will
divide
it
equally
---page break---
P.70
128
If
a
line
terminated
by a
circle
is divided
equally
by a
line
cutting
it at
right
angles
the
cutting
line
will
pass
through
the
centre
of
the
circle.
---page break---
p 71
129
If
from
a
certain
point
within
a
circle
three
equal
strait
lines
be
drawn
to the
circumference
that
point
is the
center
of the
circle.
---page break---
p 72
130
In
a
circle
equal
strait
lines
terminated
by
the
circumference
are
equally
distant
from
the
center
---page break---
p 73
131
In
a
circle
strait
lines
equally
distant
from
the
centre,
&
terminated
by
the
circumference,
are
equal
to one
another.
p 74
132
In
circles
the
greatest
line
is a
diameter,
and of
other
lines
the
nearer
to
the
centre
is
the
greater,
---page break---
p 75
133
Of
strait
lines
drawn
from
the
same
point
to the
circumference
of a
circle,
the
greatest
is
that
passing
through
its
centre,
&
the
least
falls
in the
opposite
point <lb/to the
greatest.
---page break---
p76
134
Only
two
equal
lines
can
be
drawn
to the
circumference
of a
circle,
from
any
point
which
is not
its
center
---page break---
p76
135
Corollary.
One
circle
can
cut
another
in
two
points
only
---page break---
p77
136
If
two
circles
touch
one
another,
a
strait
line
joining
their
centers
will
fall
in the
point
of
contact
---page break---
p 78
136
Case
2.
When
the
circles
touch
inwardly
a
strait
line
joining
their
centers
will
fall
in the
point
of
contact
---page break---
p78
137
Corollary.
One
circle
can
touch
another
in
one
point
only
---page break---
p79
138
A
strait
line
drawn
at
right
angles
to the
extremity
of a
diameter,
is a
tangent
to the
circle.
---page break---
p79
139
Corollary
A
strait
line
can
touch
a
circle
in
one
point
only
---page break---
p 80
140
A
line
drawn
from
the
centre
of
a
circle
to the
point
of
contact
will
be
perpendicular
to the
tangent
---page break---
p81
141
A
line
drawn
at
right
angles
to a
tangent
at
the
point
of
contact
will
pass
thro'
the
centre
of
the
circle
---page break---
p82
142
An
angle
at the
centre
of
a
circle
is
double
to
an
angle
at the
circumference
standing
upon
the
same
arch
---page break---
p. 83
143
All
angles
in
the
same
segment
of a
circle
are
equal
to
one
another
---page break---
p. 84
144
The
opposite
angles
of
any
quadrangle
inserited
in
a circle,
are
equal
to two
right
angles.
---page break---
p 85
145
Corrolarly
If any
side of
a quadrangle
inserited
in
a circle
is produced
the
outward
angles
will
be equal
to the
inward
and
opposite
angles.
---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.
Identifier: | JB/135/081/002"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 |
||
002 |
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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