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The Propositions of the third and fourth Boo
Prop I Prob.To find the Center of a given Circle.
Prop VI TheorIf two circles touch one another internally,
they shall not have the same center.
Prop X TheorOne circumference of a circle cannot cut
another in more than two points.
Prop XV TheorThe Diameter is the greatest straight line in a circle;
and of all others, that which is nearer to the Center is
always greater than one more remote: and the greater
is nearer to the Center than the less.
Prop XX TheorThe angle at the Center of a Circle is double of
the angle at the Circumference, upon the same base,
that is, upon the same part of the Circumference.
Prop XXV Prob.A Segment of a Circle being given to describe
of which it is the Segment.
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Prop II Theor.If any two points be taken in the circumference
of a Circle, the straight line which joins them shall fall within the circle.
Prop VII Theor.If any point be taken in the diameter of a circle, which
is not the center, of all the straight lines which can be
drawn from it to the circumference, the greatest is that
in which the Center is, and the other part of that
diameter is the least: and of any others, that which is nearer
to the line which passes thro' the Center is always greater
than one more remote, and from the same point there can be
drawn only two straight lines that are equal to one another
upon each side of the line.
Prop XI TheorIf two Circles touch each other internally, the straight
line which joins their centers being produced shall
pass thro' the point of contact.
Prop XVI TheorThe straight line drawn at right angles to the Diameter of a circle
from the extremity of it, falls without the Circle; & no straight
line can be drawn, between that straight line and the
circumference from the extremity, so as not to cut the circle:
or, which is the same thing, no straight line can make
so great an acute angle with the diameter at its
extremity, or so small an angle wh with the straight
line which is at right angles to it, as not to cut the circle.
Prop XXI TheorThe angles in the same Segment of a circle are
equal to one another.
Prop XXVII Theor.In equal circles, equal angles stand upon equal
circumferences, whether they be at the centers
or circumferences
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the propositions of the third and fourth books of euclid as expressed by simson |
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private material |
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sir samuel bentham |
[[watermarks::[tall thin motif with prince of wales feathers] icv]] |
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