94

SURFACE OF PLANE FIGURES.

SIXTH LESSON.

On the surface of plane figures, terminated by straightor circular lines.

When we wish to measure surfaces terminated byright lines, or even by curves, we take as the unit of ourmeasure, a simple figure, equally easy to construct ando subdivide ; viz. a square, the side of which is equal tothe unit of length.

Let us first explain how we can measure a large squarewith a small one ; or, in other words, ascertain how manytimes the large square contains the smaller one.

We can form, in the large square, as many parallelbands, as one side of the small square is contained times inone side of the large square, and these parallel bands willhave the side of the small square for their breadth, andthe side of the large square for their length. But asmany times as the side of the smaller square, is contain-ed in the side of the larger, so many times will the smal-ler square be contained in each parallel band. If, for ex-ample, the side of the larger contains the side of the smallsquare ten times, the large square is divided into ten pa-rallel bands, having the small side for their breadth : andten times the length of this side is their length. Eachband, therefore, will contain ten times the surface of thesmall square; and ten times ten will be the number ofsmall squares contained in the large one.