An Elementary Treatise on Plane and Solid Geometry |
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Common terms and phrases
ABC fig angle BAC arc BC base and altitude bisect centre chord circumference common altitude construct convex surface Corollary DEF fig Definitions denote described diameter divided Draw equal arcs equal distances equiangular with respect equilateral equivalent frustum given angle given circle given line given polygon given sides given square greater half the product Hence homologous sides hypothenuse infinite number infinitely small Inscribed Angle inscribed circle isoperimetrical isosceles Join AC line AB fig line BC mean proportional number of sides oblique lines parallel planes parallel to BC parallelogram parallelopipeds perimeter perpen perpendicular plane MN polyedron polygon ABCD &c Problem Proof pyramid or cone radii radius rectangles regular polygon right triangle Scholium secant sector segment side AC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle tangent Theorem trapezoid 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 68 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 135 - AC', BC' of the triangle ABC', symmetrical to ABC. 452. Theorem. If two triangles on the same sphere, or on equal spheres, have two sides, and the included angle of the one respectively equal to the two sides and the included angle of the other, they are equal, or else they are symmetrical. Proof. For one of the triangles may be applied to the other, or to its symmetrical triangle. 453. Theorem. In every isosceles spherical triangle the angles opposite the equal sides are equal. Proof. Let AB (fig....
Page 126 - A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a point within called the centre.
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 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 83 - Since the aggregate of the quanties neglected is infinitely small, that is, as small as we choose ; we can choose it to be less than the error A ; a manifest absurdity, for the error cannot be greater than the aggregate of the quanties neglected, and yet we cannot escape this absurdity so long as we suppose the error A to be of any magnitude whatever. 286. Definition. Similar sectors and similar segments are such as correspond to similar arcs. 287. Theorem. Similar sectors are to each other as the...
Page 5 - A Plane is a surface in which any two points being taken, the straight line joining those points lies wholly in that plane.
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'.