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An acute angle is that which is less than a right angle.
XIII. “ A term or boundary is the extremity of anything."
XIV. A figure is that which is enclosed by one or more boundaries.
XV. A circle is a plane figure contained by one line, which
is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
the centre, and terminated both ways by the circumference.
XVIII. A semicircle is the figure contained by a diameter and
the part of the circumference cut off by the di
XIX. “A segment of a circle is the figure contained by a
straight line, and the circumference it cuts off.”
Rectilineal figures are those which are contained by
XXI. Trilateral figures, or triangles, by three straight lines.
Quadrilateral figures, by four straight lines.
Multilateral figures, or polygons, by more than four straight lines.
angle is that which has three equal sides.
XXV. An isosceles triangle is that which has only two sides equal.
XXVI. A scalene triangle is that which has three unequal sides.
XXVII. A right-angled triangle is that which has a right angle.
three acute angles.
has all its sides equal, and all its angles
An oblong, or rectangle, is that which has
all its angles right angles, but has not all its sides equal.
A rhombus is that which has all its
sides equal, but its angles are not right angles.
A rhomboid is that which has its op
posite sides equal to one another, but all its sides are not equal, nor its angles right angles.
XXXIV. Any other four-sided figure, besides these, is called a
XXXV. Parallel straight lines are such as are in the saine
plane, and which, however far produced either way, do not meet.
Let it be granted, that a straight line may be drawn from any one point to any other point.
II. That a terminated straight line may be produced to any length in a straight line.
III. And that a circle may be described from any centre,
at any distance from that centre.
1. Things which are equal to the same thing, are equal to one another.
III. If equals be taken from equals, the remainders are equal.
IV. If equals be added to unequals, the wholes are unequal.
V. If equals be taken from unequals, the remainders are
VI. Things which are double of the same, are equal to one another.
VII. Things which are halves of the same, are equal to one another.
VIII. Magnitudes which coincide with one another, that is,
which exactly fill the same space, are equal to one another.
Two straight lines cannot enclose a space.
All right angles are equal to one another.
XII. “ If a straight line meet two straight lines, which are
“ in the same plane, so as to make the two interior “ angles on the same side of it, taken together, less “ than two right angles, these straight lines being “ produced, shall at length meet upon that side on “ which are the angles which are less than two “ right angles."