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<head><!-- Pencil heading -->N<hi rend="superscript">o</hi> 125. p.67</head>
<p><!-- Pencil heading -->N<hi rend="superscript">o</hi> 125. p.67</p>
<head>p.67<lb/>
<p>p.67<lb/>
125</head><lb/>
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><pb/>
circle</p>


<head>p.68 <lb/>
<pb/>
126</head>  
<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>


<head>p 69<lb/>
<pb/>
127</head><lb/>
<p>p 69<lb/>
127</p>
<lb/>
<p>A<lb/>
<p>A<lb/>
line<lb/>
line<lb/>
Line 66: Line 68:
to  a<lb/>
to  a<lb/>
line<lb/>
line<lb/>
termiated<lb/>
terminated<lb/>
by<lb/>
by<lb/>
the<lb/>
the<lb/>
Line 73: Line 75:
divide<lb/>
divide<lb/>
it<lb/>
it<lb/>
equally</p><pb/>
equally</p>
 
<head>P.70<lb/>
128</head>


<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><pb/>
circle.</p>


<pb/>
<p>p 71<lb/>
<p>p 71<lb/>
129</p>
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>


<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 circumference <lb/>that <lb/>point <lb/>is the <lb/>center <lb/>of the <lb/>circle.</p><pb/>
<pb/>
 
<p>p 72<lb/>
<p>p 72<lb/>
130</p>
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>


<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/>
<pb/>
 
<p>p 73<lb/>
<p>p 73<lb/>
131</p>
131</p>
<p>In <lb/>
a <lb/>
circle <lb/>
strait <lb/>
lines <lb/>
equally <lb/>
distant <lb/>
from <lb/>
the <lb/>
centre, <lb/>
&amp; <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/>
&amp;<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>


<p>In <lb/>a <lb/>circle <lb/>strait <lb/>lines <lb/>equally <lb/>distant <lb/>from <lb/>the <lb/>centre, <lb/>&amp; <lb/>terminated <lb/>by <lb/>the <lb/>circumference,<lb/>are <lb/>equal <lb/>to one <lb/>another.</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>  


<p>p 74<lb/>
<pb/>
132</p>
<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>


<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/>
<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>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/>&amp;<lb/>the <lb/>least <lb/>falls i<lb/>n the <lb/>opposite <lb/>point <lb/to the <lb/>greatest.</p><pb/>
<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>


<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/>
<pb/>
centre</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>


<p>p76<lb/>135</p> Corollary. <lb/>
<pb/>
<p>One <lb/>circle <lb/>can <lb/>cut <lb/>another <lb/>in <lb/>two <lb/>points <lb/>only</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>


<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/>
<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>


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{{Metadata:{{PAGENAME}}}}
{{Metadata:{{PAGENAME}}}}{{Completed}}

Latest revision as of 10:35, 4 February 2020

Click Here To Edit

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.

Date_1

Marginal Summary Numbering

Box

135

Main Headings

posology

Folio number

081

Info in main headings field

geometry i

Image

002

Titles

no. 125 p. 67

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

46199

Box Contents

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