An Elementary Treatise on Plane and Solid Geometry |
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Common terms and phrases
ABC fig AC AC adjacent angles altitude angle BAC arc BC base and altitude bisect centre chord circumference construct convex surface Corollary cylinder DEF fig Definitions denote diameter divided equal arcs equal distances equiangular with respect equilateral equivalent frustum given angle given circle given line given polygon given ratio given square gles greater half the arc half the product Hence homologous sides hypothenuse infinite number Inscribed Angle inscribed circle isosceles Join AC Let ABCD line AB fig line BC mean proportional number of sides oblique lines parallel planes parallelogram parallelopipeds perimeter perpendicular point of division polyedron polygon ABCD &c prism Problem Proof radii rectangles regular polygon right triangle Scholium secant sector segment side BC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle straight line tangent Theorem trapezoid triangle ABC vertex vertices whence
Popular passages
Page 143 - 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 26 - 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 22 - The sum of the three angles of any triangle is equal to two right angles.
Page 18 - Theorem. In an isosceles triangle the angles opposite the equal sides are equal.
Page 89 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Page 33 - Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords.
Page 19 - Jl will be equal to C. 56. Corollary. An equilateral triangle is also equiangular. 57. Theorem. The line BD (fig. 32), which...
Page 70 - 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 73 - Rectangles of the same altitude are to each other as their bases, and rectangles of the same base are to each other as their altitudes. 245.
Page 137 - ... equal as to the magnitude of those parts. Hence, those two triangles, having all their sides respectively equal in both, must either be absolutely equal, or at least symmetrically so; in both of which cases their corresponding angles must be equal, and lie opposite to equal sides.