An Elementary Treatise on Plane and Solid GeometryWilliam H. Dennet, 1872 |
Contents
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Common terms and phrases
ABC fig adjacent angles altitude angle BAC arc BC base and altitude bisect CD fig centre chord circumference coincide construct convex surface Corollary cylinder DEF fig Definitions denote diameter divided Draw equal arcs equal distances equiangular with respect equilateral equivalent frustum given angle given circle given line given polygon given ratio given sides given square gles greater half the product Hence homologous sides hypothenuse included angle infinite number Inscribed Angle inscribed circle Join AC line AB fig line BC mean proportional number of sides oblique lines parallel lines parallelogram parallelopipeds perimeter perpendicular polyedron polygon ABCD &c prism Problem Proof radii radius rectangles regular polygon respectively equal rhombus right triangle Scholium secant sector segment side AC similar polygons similar triangles solid angle Solution sphere spherical triangle tangent Theorem trapezoid triangles ABC triangular prism vertex vertices whence ᎯᏴ
Popular passages
Page 133 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
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 80 - Problem. To construct a polygon similar to a given polygon, and having a given ratio to it.
Page viii - A line parallel to one side of a triangle divides the other two sides proportionally.
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 34 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
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 130 - Each side of a spherical triangle is less than the sum of the other two sides.
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 6 - Your geometry states it as an axiom that a straight line is the shortest way from one point to another; and astronomy shows you that God has given motion only in curves.