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A See

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1. Point is that which has position, but not magnitude;"* (See Notes.)

II. A line is length withbut breadth.

“Corollary. The extremities of a line are points; and the ina * tersections of one line with another are also points.”

III. 6 If two lines are such that they cannot coincide in any two points, ś without coinciding altogether, each of them is called a straight line.”

“ Cor. Hence two straight lines cannot enelose a space. Neither can two straight lines have a common segment; that is, they cannot 6 coincide in part, without coinciding altogether."

IV.
A superficies is that which has only length and breadth.

“Cor. The extremities of a superficies are lines; and the intet. sections of one superficies with another are also lines."

V. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies.

VI.

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.

* The definitions marked with inverted commas are different from those of Euclid.

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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 vers

tex of the angle, that is, at the point in which the straight lines that 6 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 (he 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, BD is named the angle ABD,

or DBA; and that which is contained by BD, 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.?

VII.
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.

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

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

X.
A figure is that which is enclosed by one or more boundaries.- The

word area denotes the quantity of space contained in a figure, without any reference to the nature of the line or lines which bound it.

XI. 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 cer. tain 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 straight line drawn through the centre, and terminated both ways by the circumfereace.

XIV. A semicircle is the figure contained by a diameter and the part of the

circuinference cut off by the diameter.

XV.

Rectilineal figures are those which are contained by straight lines.

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

XVII.
Quadrilateral, by four straight lines.

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

XIX. or three sided figures, an equilateral triangle is that which has three equal sides.

XX.
An isosceles triangle is that which has only two sides equal.

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XXI
A scalene triangle, is that which has three unequal sides.

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

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

XXIV.
An acute angled triangle, is that which bas three acute angles.

XXV. of four sided figures, a square is that which has all its sides equal, and all its angles right angles.

XXVI. An oblong, is that wbich has all its angles right angles, but has not all its sides equal

XXVII. A rhombus, is that which has all its sides equal, but its angles are not

right angles.

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XXVIII. 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.

XXIX.
All other four sided figures besides these, are called Trapeziums.

XXX.
Parallel straight lines, are such as are in the same plane, and which

being produced eper so far both ways, 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.

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 doubles of the same thing, are equal to one another,

VII. Things which are halves of the same 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.

XI. $6 Two straight lines wbich intersect one another, cannot be both

parallel to the same straight line."

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