Books of Euclid as expressed by Simson.
be draw thro the Center of
raight line in it, which
the Center, it shall cut it
it cuts it at right angles
Prop VIII Theor.
thout a Circle and straight lines be drawn from it to the circumference, whereof one
those which fall upon the concave circumference the greatest is that which passes
the rest, that which is nearer to that thro' the center is always greater than the
those which fall upon the convex circumference, the least is that between the
le and the diameter: and of the rest that which is nearer to the least is always
emote, and only two equal straight lines can be drawn from the point unto
one upon each side of the least.
ach other externally, the straight
ters shall pass thro’ the point of
line from a given point, either
Circumference, which shall
of any quadrilateral fig-
circle, are together equal to
the angles which stand upon
are equal to one another
the centers or circumfe-
Prop IV Theor.
If in a Circle two straight lines cut one another,
which do not both pass thro' the Center, they do
not bisect each the other.
Prop XIII Theor.
One circle cannot touch another in more points
than one, whether it touches it on the inside or
Prop XVIII Theor.
If a straight line touches a circle, the straight
line drawn from the Center to the point of Contact,
shall be perpendicular to the line touching the
Prop XXIII Theor.
Upon the same straight line & upon the same
side of it, there cannot be two similar segments
of circles, not coinciding with one another
Prop XXVII Theor.
In equal circles equal straight lines cut off equal
circumferences, the greater equal to the greater
and the less to the less.
Prop V Theor
If two circles cut one, they shall not have
the same center.—
Prop IX Theor.
If a point be taken within a circle, from which
there fall more than two equal straight lines to
the circumference, that point is the Center of
Prop XIV Theor.
Equal straight lines in a Circle are equally distant
from the Center; & those which are equally distant
from the Center are equal to one another.—
Prop XIX Theor
If a straight line touches a Circle, & from the point
of contact a Straight line be drawn at right
angles to the touching line, the Center of the circle
shall be in that line.
Prop XXIV Theor.
Similar Segments of circles upon equal
straight lines are equal to one another.
Prop XXIX Theor.
In equal circles equal circumferences are
subtended by equal straight lines.
Identifier: | JB/135/073/003
"JB/" can not be assigned to a declared number type with value 135.
the propositions of the third and fourth books of euclid as expressed by simson
sir samuel bentham
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