Plane Geometry, Practical and Theoretical; Books I. II. III. Volume 1 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 edition. Excerpt: ...may have three bases, it consequently has three altitudes, namely, the perpendiculars drawn from the three vertices to the opposite sides. Also, since parallel straight lines are equidistant from each other, it comes to the same thing to say that parallelograms or triangles have the same or equal altitudes as to say that they are (or can be placed) between the same parallels. 3. The size of the surface, or in other words the area, of a closed rectilineal figure is obtained by finding how often this surface contains another given surface, which is gener ally in the form of a square, such as a square inch, a square centimetre, &c. Take, for example, the rectangle ACDB, whose adjacent sides AB, AC (called respectively the length and breadth) are 4 and 3 inches. A B C D If AB be divided into 4 equal parts, and AC into 3 equal parts, and if through the points of division on AB parallels be drawn to AC, and through the points of division on AC parallels be drawn to AB, a series of small squares are formed whose sides are 1 inch long. Seeing that there are 4 squares in each row, and that there are 3 rows, the number of squares is 4 x 3, or 12. Hence we say that the area of the rectangle AB-AC=12 sq. in. This procedure suggests the rule for finding the area of a rectangle: Express the length and the breadth of the rectangle in the same units. Multiply the number of units in the length by the number of units in the breadth, and the result will be the number of square units in the area. Since a squam is a rectangle whose length and breadth are equal, the application of the rule will show us that the area of a square whose side is 2 inches is (2 X 2) times the area of a square whose side is 1 inch; that the area of a square whose side is...