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VIII.

See N.

A plane angle is the inclination of two lines to one

6 another in a plane, which meet together, but are
66 not in the same direction.”

IX.
A plane rectilineal angle is the inclination of two

straight lines to one another, which meet together,
but are not in the same straight line.

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N. B. · When several angles are at one point B, any one of them is expressed by three letters, of which • the letter that is at the vertex of the angle, that is, at 'the point in which the straight lines that contain the

angle meet one another, is put between the other two • letters, and one of these two is somewhere upon one

of those straight lines, and the other upon the other • line: Thus the angle which is contained by the straight lines, AB, CB, is named the angle ABC, or CBA; that which is contained by AB, DB is named the angle ABD, or, DBA; and that which is contained by · DB, CB, is called the angle DBC, or CBD; but, if

there be only one angle at a point, it may be expressed by a letter placed at that point: as the angle at E.'

X.
When a straight line standing on another

straight line makes the adjacent angles
equal to one another, each of the angles
is called a right angle; and the straight
line which stands on the other is called
a perpendicular to it.

XI.
An obtuse angle is that which is greater than a right

angle.

XII.

An acute angle is that which is less than a right angle.

XIII. “ A term or boundary is the extremity of any thing.”

XIV.
A figure is that which is enclosed by one or more boun-
daries.

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 See N.

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 diameter.

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, by four straight lines.

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

XXIV.
Of three-sided figures, an equilateral triangle is that

which has three equal sides.

XXV.
An isosceles triangle is that which has only two sides

equal.

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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.

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XXIX.
An acute angled triangle, is that which has three acute
angles.

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

sides equal, and all its angles right angles.

XXXI.
An oblong 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.

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See N.

XXXIII.
A rhomboid, is that which has its opposite sides equal

to one another, but all its sides are not equal, nor
its angles right angles.

XXXIV. All other four-sided figures besides these, are called trapeziums.

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

plane, and which being produced ever so far boch ways, do not meet.

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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

circle
may

be described from any centre at any distance from that centre.

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AXIOMS.

I. 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 inclose a space.

XI.
All right angles are equal to one another.

XII. “ If a straight line meet two straight lines, so as to

6 make the two interior angles on the same side of “ it taken together less than two right angles, these “ straight lines being continually produced, shall at “ length meet upon that side on which are the

angles “ which are less than two right angles."

See the notes on Prop. 29. of Book 1.

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