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DEFINITIONS.

1. Point is that which hath no parts, or which hath no mage Sec Notes. nitude.

II. A line is length without breadth.

III. The extremities of a line are points.

IV.
A straight line is that which lies evenly between its extreme
points.

V.
A superficies is that which hath only length and breadth.

VI.
The extremities of a superficies are lines.

VII. A plane superficies is that in which any two points being taken, See N. che ftraight line between them lies wholly in that superficies.

VIII. " A plane angle is the inclination of two lines to one another See N.

" in a plane, which meet together, but are 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
fame straight line.

N. B.

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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 "js 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 expreffed by a letter placed at that point ; ( as the Angle at E.'

X.
When a straight line' ftanding on ano-

ther 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 angles

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 inclosed by one or more boundaries.

XV.

OF EUCLI D.

Book 1.

XV.
A circle is a plane figure contained by one line, which is cal.

led the circumference, and is such that all straight lines
drawn from a certain point within the figure to the circum-
ference, are equal to one another :

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XVI. 354 And this point is called the centre of the circle.

XVII. A diameter of a circle is a straight line drawn through the See N. 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 lided figures, an equilateral triangle is that which has
three equal fides.

XXV.
An isosceles triangle, is that which has only two fides equal.

XXVI.

Book I.

ΔΔΔ

XXVI.
A scalene triangle, is that which bas three unequal Gdes.

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 fided figures, a square is that which has all its fides

equal, and all its angles right angles.

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

XXXII.
A rhombus, is that which has all its &des equal, but its angles

are not right angles.

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XXXIII. See N. A rhomboid, is that which has its opposite sides equal to one

another, but all its fides are not equal, nor its angles right angles.

XXXXIV

OF EUCLID.

13

Book I.

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

Xxxv.
Parallel straight lines, are such as are in the fame plane, and

which, being produced ever so far both ways, do not meet.

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L

1.
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 cisele may be described from any centre, at any distance from that centre.

A X I OM S.

TH

ES,

1.
HINGS which are equal to the same are equal to one an.
other,

11.
If equals be added to equals, the wholes are equal.
If equals be taken from equals, the remainders are equal

IV.
If equals be added to unequals, the wholes are unequal.

y.
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
esadly fill the same space, are equal to one another.

IX.

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