# Book I.

## Definitions.

### I.

A *point* is that which has no parts.

### II.

A *line* is length without breadth.

### III.

The extremities of a line are points.

### IV.

A ſtraight or right line is that which lies evenly between its extremities.

### V.

A ſurface is that which has length and breadth only.

### VI.

The extremities of a ſurface are lines.

### VII.

A plane ſurface is that which lies evenly between its extremities.

### VIII.

A plane angle is the inclination of two lines to one another, in a plane, which meet together, but are not in the ſame direction.

### IX.

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

### X.

When one ſtraight line ſtanding on another ſtraight line makes the adjacent angles equal, each of theſe angles is called a *right angle*, and each of theſe lines is ſaid to be *perpendicular* to the other.

### XI.

An obtuſe angle is an angle greater than a right angle.

### XII.

An acute angle is leſs than a right angle.

### XIII.

A term or boundary is the extremity of any thing.

### XIV.

A figure is a ſurface encloſed on all ſides by a line or lines.

### XV.

A circle is a plane figure, bounded by one continued line, called its circumference or periphery; and having a certain point within it, from which all ſtraight lines drawn to its circumference are equal.

### XVI.

This point (from which the equal lines are drawn) is called the centre of the circle.

### XVII.

A diameter of a circle is a ſtraight line drawn through the centre, terminated both ways in the circumference.

### XVIII.

A ſemicircle is the figure contained by the diameter, and the part of the circle cut off by the diameter.

### XIX.

A ſegment of a circle is a figure contained by a ſtraight line, and the part of the circumference which it cuts off.

### XX.

A figure contained by ſtraight lines only, is called a rectilinear figure.

### XXI.

A triangle is a rectilinear figure included by three ſides.

### XXII.

A quadrilateral figure is one which is bounded by four ſides. The ſtraight lines and connecting the vertices of the oppoſite angles of a quadrilateral figure, are called its diagonal.

### XXIII.

A polygon is a rectilinear figure bounded by more than four ſides.

### XXIV.

A triangle whoſe three ſides are equal, is ſaid to be equilateral.

### XXV.

A triangle which has only two ſides equal is called an iſoſceles triangle.

### XXVI.

A ſcalene triangle is one which has no two ſides equal.

### XXVII.

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

### XXVIII.

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

### 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.

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

### XXXII.

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

### 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 quadrilateral figures are called trapeziums.

### XXXV.

Parallel ſtraight lines are ſuch as are in the ſame plane, and which being produced continually in both directions, would never meet.