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| Line 66: | Line 66: | ||
to a<lb/> | to a<lb/> | ||
line<lb/> | line<lb/> | ||
terminated<lb/> | |||
by<lb/> | by<lb/> | ||
the<lb/> | the<lb/> | ||
| Line 104: | Line 104: | ||
circle.</p><pb/> | circle.</p><pb/> | ||
< | <head>p 71<lb/> | ||
129</ | 129</head> | ||
<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/> | <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/> | ||
< | <head>p 72<lb/> | ||
130</ | 130</head> | ||
<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>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/> | ||
< | <head>p 73<lb/> | ||
131</ | 131</head> | ||
<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>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> | ||
< | <head>p 74<lb/> | ||
132</ | 132</head> | ||
<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>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/> | ||
< | <head>p 75<lb/>133</head> | ||
<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/> | |||
<head>p76 <lb/>134</head> | |||
<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/> | |||
< | <head>p76<lb/>135</head> <p>Corollary. <lb/>One <lb/>circle <lb/>can <lb/>cut <lb/>another <lb/>in <lb/>two <lb/>points <lb/>only</p> <pb/> | ||
< | <head>p77 <lb/>136</head> <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/> | ||
< | <head>p 78<lb/>136</head> | ||
<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/> | <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/> | point <lb/>of <lb/>contact</p><pb/> | ||
<p>p79 <lb/>138</ | <head>p78 <lb/>137</head> <p>Corollary. <lb/>One <lb/>circle <lb/>can <lb/>touch <lb/>another <lb/>in <lb/>one <lb/>point <lb/>only</p><pb/> | ||
<head>p79 <lb/>138</head> <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/> | |||
< | <head>p79 <lb/>139</head> <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/> | ||
< | <head>p 80 <lb/>140</head> <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/> | ||
< | <head>p81 <lb/>141</head> <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/> | ||
< | <head>p82 <lb/>142</head> <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/> | ||
< | <head>p83 <lb/>143</head> <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/> | ||
< | <head>p84 <lb/>144</head> <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/> | ||
< | <head>p 85 <lb/>145</head> <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/> | ||
< | <head>p 85 <lb/>146</head> <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> <pb/> | ||
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---
p83
143
All
angles
in
the
same
segment
of a
circle
are
equal
to
one
another
---page break---
p84
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
---page break---
|
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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copy/fair copy sheet |
3 |
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recto |
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46199 |
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