Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

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Ivison, Phinney, Blakeman & Company, 1868 - Geometry - 262 pages

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Page 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 96 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 128 - To inscribe a regular polygon of a certain number of sides in a given circle, we have only to divide the circumference into as many equal parts as the polygon has sides : for the arcs being equal, the chords AB, BC, CD, &c.
Page 174 - A cylinder is conceived to be generated by the revolution of a rectangle about one of its sides as an axis.
Page 254 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 77 - FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi.
Page 113 - From a given point, to draw a line parallel to a given line. Let A be the given point, and BC the given line.
Page 160 - THEOREM. If two planes are perpendicular to the same straight line, they are parallel to each other. Let the planes MN...
Page 58 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 61 - A fourth proportional to three quantities is the fourth term of a proportion, whose first three terms are the three quantities taken in their order. Thus, in the proportion a : b = c : d, d is a fourth proportional to a, b, and c.

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