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ERRATA.

Book III. Definitions, for Def. XI. read Def. IX.

Book V. Prop. XXIV. line third of the Demonstration, read Because E:B::F: D, by inverfion, B: E::C:D.

P. 263. fourth line, for a, read two.

ELEMENTS

OF

GEOMETRY.

“A

BOOK I.

DEFINITIONS.

I.

Point is that which has pofition, but not magni- See Notes. tude."

II.

A line is length without breadth.

COROLLARY. The extremities of a line are points; and "the intersections of one line with another are also points."

III.

"Lines which cannot coincide in two points, without coinciding altogether, are called straight lines.

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"COR. Hence two straight lines cannot inclose a space. Nei"ther can two ftraight lines have a common fegment; "that is, they cannot coincide in part, without coinciding S altogether."

IV.

A fuperficies is that which hath only length and breadth.
"COR. The extremities of a fuperficies are lines; and the
"interfections of one fuperficies with another are alfo lines.”

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

VI.

A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the fame ftraight line.

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N. B. When several angles are at one point B, any one of them is expreffed 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 ftraight lines AB, CB, is named the angle ABC, of 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 expreffed by a letter placed at that point; as the angle at E.

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VII.

When a ftraight line standing on an-
other ftraight line makes the adja-
cent angles equal to one another,
each of the angles is called a right
angle; and the ftraight line which
ftands on the other is called a per-
pendicular to it.

VIII.

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

Book I.

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 straight 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.

XV.

Rectilineal figures are those which are contained by straight

lines.

XVI.

Trilateral figures, or triangles, by three ftraight lines.

XVII.

Quadrilateral, by four straight lines.

XVIII.

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

ΧΙΧ.

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

XX.

An isofceles 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.

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

XXIII.

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

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