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XII.

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.

XVI.
And this point is called the centre of the circle.

XVII.
A diameter of a circle is a straight line drawn through

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

ameter.

XIX. A segment of a circle is the figure contained by a

straight line, and the circumference it cuts off.”

XX.

Rectilineal figures are those which are contained by

straight lines.

XXI. Trilateral figures, or triangles, by three straight lines.

XXII.

Quadrilateral figures, by four straight lines.

XXIII.

Multilateral figures, or polygons, by more than four straight lines.

XXIV.
Of three-sided figures, an equilateral tri-

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.

XXVIII.
An obtuse angled triangle is that which
has an obtuse angle.

XXIX.
An acute-angled triangle is that which has

three acute angles.

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XXX.
Of four-sided figures, a square is that which

has all its sides equal, and all its angles
right angles.

XXXI.

An oblong, or rectangle, is that which has

all its angles right angles, but has not all its sides equal.

XXXII.

A rhombus is that which has all its

sides equal, but its angles are not right angles.

XXXIII.

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

trapezium.

XXXV. Parallel straight lines are such as are in the saine

plane, and which, however far produced either way, do not meet.

POSTULATES.

I.

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.

AXIOMS.

1. Things which are equal to the same thing, are equal to one another.

II.
If equals be added to equals, the wholes are equal.

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

unequal.

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.

IX.
The whole is greater than its part.

X.

Two straight lines cannot enclose a space.

XI.

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."

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