An Elementary Treatise on Plane and Solid Geometry |
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Common terms and phrases
ABC fig adjacent angles angle BAC arc BC base and altitude bisect centre chord circumference common altitude 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 gles greater half the product Hence homologous sides hypothenuse infinite number infinitely small inscribed circle isoperimetrical isosceles Join AC line AB fig line BC mean proportional number of sides oblique lines parallel lines parallel to BC parallelogram parallelopipeds perimeter perpendicular plane MN polyedron polygon ABCD &c Problem Proof pyramid or cone radii radius rectangles regular polygon right triangle Scholium secant sector segment side BC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle tangent Theorem trapezoid triangles ABC triangular prism vertex vertices whence ᎯᏴ
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 74 - The square described upon the hypothenuse of a right triangle is equivalent to the sum of the squares described upon the other two sides.
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 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 viii - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 80 - Problem. To construct a polygon similar to a given polygon, and having a given ratio to it.
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 16 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 87 - To construct a parallelogram equivalent to a given square, and having the difference of its base and altitude equal to a given line.
Page 34 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.