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VIII.

An obtufe angle is that which is greater than a right angle.

IX.

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

X.

A figure is that which is inclosed by one or more boundaries.

XI."

A circle is a plane figure contained by one line, which is called the circumference, and is fuch that all ftraight lines drawn from a certain point within the figure to the circumference, are equal to one another.

XII.

And this point is called the centre of the circle.

XIII.

A diameter of a circle is a ftraight line drawn through the centre, and terminated both ways by the circumference.

XIV.

A femicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter.

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Book I.

Book I.

XV.

Rectilineal figures are those which are contained by straight

lines.

XVI.

Trilateral figures, or triangles, by three ftraight lines.

XVII.

Quadrilateral, by four ftraight lines.

XVIII.

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

XIX.

Of three fided figures, an equilateral triangle is that which has three equal fides.

XX.

An ifofceles triangle is that which has only two fides equal.

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XXI.

A fcalene triangle, is that which has three unequal fides.

XXII.

right angled triangle, is that which has a right angle.

XXIII.

An obtuse angled triangle, is that which has an obtuse angle,

XXIV.

XXIV.

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

XXV.

Of four fided figures, a fquare is that which has all its fides equal, and all its angles right angles.

Book I.

XXVI.

An oblong, is that which has all its angles right angles, but has not all its fides equal.

XXVII.

A rhombus, is that which has all its fides equal, but its angles are not right angles.

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XXVIII.

A rhomboid, is that which has its oppofite fides equal to one another, but all its fides are not equal, nor its angles right angles.

XXIX.

All other four fided figures befides thefe, are called Tra

peziums.

B 3

XXX.

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Parallel straight lines, are fuch as are in the fame plane, and which, being produced ever fo far both ways, do not meet.

L

POSTULATES.

I.

ET 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.

AXIOM S.
I.

HINGS which are equal to the fame thing are equal to one another.

N.

THI

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,

VI.

Things which are doubles of the fame thing, are equal to one another.

VII.

Things which are halves of the fame thing, 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.

All right angles are equal to one another.

"Two straight lines, which interfect one another, cannot be "both parallel to the same straight line."

Book I.

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