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No 125 p. 67
A strait line that joins any two
points in the circumference of a
circle, will fall within the circle.
No 126 p. 68
A line drawn from the center
of a circle, to the middle of a line
terminated by the circumference,
will meet the same at right angles.
No 127 p 69
A line drawn from the center of
a circle, at right angles to a line
terminated by the circumference,
will divide it equally.
No 128 p. 70
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
center of the circle.
No 129 p. 71
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.
No 130 p. 72
In a circle, equal strait lines
terminated by the circumference
are equally distant from the
center.
No 131 p. 73
In a circle, strait lines equally
distant from the center, and terminated
by the circumference,
are equal to one another.
No 132 p. 74
In circles, the greatest line is
a diameter, and of other lines
the nearer to the center is the greater.
No 133 p. 75.
Of strait lines drawn from the
same point to the circumference
of a circle, the greatest is that
passing through its center, and
the least falls in the opposite
point to the greatest.
No 134 p. 76
Only two equal lines can be
drawn to the circumference of
a circle, from any point which
is not its center.
No135 p. 76
Corollary
One circle can cut another in two
points only.
No136 p. 77
If two circles touch one another,
a strait line joining their centers
will fall in the point of contact.
No 136 p. 78
Case. 2. When the circles touch
inwardly a strait line joining
their centers will fall in the
point of contact.
No 137 p. 78
Corollary
One circle can touch another in
one point only.
No 138 p. 79
A strait line drawn at right
angles to the extremity of a
diameter, is a tangent to the
circle.
No139 p. 79
Corollary
A strait line can touch a circle
in one point only.
No 140 P. 80
A line drawn from the center of a
circle to the point of contact, will
be perpendicular to the tangent.
No 141 p. 81
A line drawn at right angles to
a tangent, at the point of contact,
will pass thro' the center of the
circle.
No 142 p. 82
An angle at the center of a
circle is double to an angle at
the circumference, standing up
on the same arch.
No 143 p 83
All angles in the same segment
of a circle, are equal to
one another.
No144 p 84
The opposite angles of any quadrangle
inscribed in a circle, are
equal to two right angles.
No 145 p. 85
Corollary
If any side of a quadrangle inscribed
in a circle is produced, the
outward angle will be equal to the
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