Elements of Geometry, Plane and Spherical: With Numerous Practical ProblemsIvison, Phinney, Blakeman & Company, 1869 |
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Common terms and phrases
AB² ABCD 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 intersect isosceles Let ABC line drawn 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 Robinson's SCHOLIUM secant segment semi-polygon side AC slant height solid angles sphere spherical polygon spherical triangle square described straight line tangent three angles triangle ABC triangular prisms vertex vertical angle volume
Popular passages
Page 56 - 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 39 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 28 - 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 253 - 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 121 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Page 111 - 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 172 - A cylinder is conceived to be generated by the revolution of a rectangle about one of its sides as an axis.
Page 94 - 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 75 - 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 127 - If the vertices of a regular inscribed polygon are joined with the middle points of the arcs subtended by the sides of the polygon, the joining lines will form a regular inscribed polygon of double the number of sides.