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distant ordinates, first given by the late Mr Thomas Weddle, in the Cambridge and Dublin Mathematical Journal, New Series, Vol. IX. p. 79. When the first, second, third, fourth, or fifth order of differences of the ordinates is constant, this method will furnish the area of the figure exactly. The tables of triangles will be useful in the construction of problems for class practice. A few examples are added on the application of Algebra to Geometry, to induce the aspiring student to step out from the beaten path of Arithmetic; for no one must consider himself proficient till he can investigate his own methods.

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MENSURATION.

DEFINITIONS.

` I. A POINT is that which has no parts, or which has no magnitude.

2. A line is length without breadth.

3. The extremities of a line are points.

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

5. A superficies is that which has length and breadth.

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

7. 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.

T. M.

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I2. And this point is called the centre of the circle (C).

13. A radius is a straight line drawn from the centre to the circumference (CD).

14.

A diameter is a straight line drawn through the centre, and terminated both ways by the circumference (AB).

15. A semicircle is the figure contained by a diameter and part of the circumference cut off by the diameter (ADB).

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