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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/>  | ||
<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><pb/>  | angles.</p>  | ||
<pb/>  | |||
<p>p 69<lb/>  | |||
127</p>  | |||
<lb/>  | |||
<p>A<lb/>  | |||
line<lb/>  | |||
drawn<lb/>  | |||
from<lb/>  | |||
the<lb/>  | |||
centre<lb/>  | |||
of<lb/>  | |||
a circle<lb/>  | |||
at<lb/>  | |||
right<lb/>  | |||
angles<lb/>  | |||
to  a<lb/>  | |||
line<lb/>  | |||
terminated<lb/>  | |||
by<lb/>  | |||
the<lb/>  | |||
circumference<lb/>  | |||
will<lb/>  | |||
divide<lb/>  | |||
it<lb/>  | |||
equally</p>  | |||
<pb/>  | |||
<p>P.70<lb/>  | |||
128</p>  | |||
<p>If<lb/>  | |||
a <lb/>  | |||
line <lb/>  | |||
terminated<lb/>  | |||
by a<lb/>  | |||
circle<lb/>  | |||
is divided<lb/>  | |||
equally<lb/>  | |||
by a<lb/>  | |||
line<lb/>  | |||
cutting<lb/>  | |||
it at<lb/>  | |||
right<lb/>  | |||
angles <lb/>  | |||
the<lb/>  | |||
cutting <lb/>  | |||
line<lb/>  | |||
will<lb/>  | |||
pass<lb/>  | |||
through<lb/>  | |||
the <lb/>  | |||
centre <lb/>  | |||
of<lb/>  | |||
the <lb/>  | |||
circle.</p>  | |||
<pb/>  | |||
<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>  | |||
<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>  | |||
<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>  | |||
<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}}}}{{Completed}}  | ||
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  | 
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 002  | 
 no. 125 p. 67  | 
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