An Elementary Treatise on Plane and Solid Geometry |
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adjacent angles altitude angle BAC arc BC base and altitude bisect CD fig centre chord circumference coincide convex surface Corollary DEF fig Definitions denote described diameter divided Draw equal arcs equal distances equiangular with respect equilateral equivalent four right angles frustum given angle given circle given line given point given polygon given sides given square gles greater half the product Hence homologous sides hypothenuse infinite number infinitely small Inscribed Angle inscribed circle isosceles line AB fig line BC mean proportional number of sides oblique lines parallel lines parallelogram parallelopipeds perimeter perpendicular polygon ABCD &c preceding Problem Proof pyramid or cone radii radius rectangles regular polygon respectively equal right triangle Scholium secant sector segment side BC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle tangent Theorem triangles ABC triangular prism vertex vertices whence
Popular passages
Page 141 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 127 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.
Page 20 - The sum of the three angles of any triangle is equal to two right angles.
Page xv - The first term of a ratio is called the antecedent, and the second term the consequent.
Page 141 - Theorem. The surface of a spherical triangle is measured by the excess of the sum of its three angles over two right angles, or 180°. Proof. Let ABC (fig. 190) be the given triangle. Produce AC to form the circumference AC AC', also produce AB and BC to form the semicircumferences ABA and CBC'.
Page 31 - Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords.
Page 24 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 7 - BAC, the letter A which is at the vertex being placed in the middle ; or the letter A may be used by itself, when this can be done without confusion. 20. Definition. When one straight line meets or -crosses another,- so as to make the two adjacent angles equal, each of these angles is called a Right angle, and the lines are said to be perpendicular to each other. Thus the angles ABC and ABD (fig'.
Page 87 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Page 99 - B, from the plane. 320. Theorem. Oblique lines drawn from a point to a plane at equal distances from the perpendicular are equal; and of two oblique lines unequally distant the more remote is the greater.