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

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ABē ABCD ACē altitude angle ABC axis base and altitude bisected chord circ circumference circumscribed polygon common cone convex surface cylinder diagonal diameter dicular distance divided draw equal altitudes equal and parallel equal angles equal bases equal sides equation equiangular equivalent four magnitudes frustum given line greater half Hence the theorem homologous edges hypotenuse interior angles isosceles Let ABC line drawn lune measured middle point multiplied number of sides opposite angles parallel lines parallelogram parallelopipe parallelopipedon pendicular perimeter perpen perpendicular plane ST polyedron PROB PROBLEM produced proportion PROPOSITION prove radii radius regular polygon right angles right-angled triangle SCHOLIUM secant segment semi-polygon slant height solid angles sphere spherical polygon spherical triangle square described straight line tangent three angles triangle ABC triangular prisms triedral angles vertex vertical angle volume

### Popular passages

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.