## An Elementary Treatise on Plane and Solid Geometry1870 |

### Other editions - View all

### Common terms and phrases

ABC fig AC AC adjacent angles altitude angle BAC arc BC bisect CD fig centre circumference coincide convex surface Corollary cylinder DEF fig Definitions denote diameter equal arcs equal distances equiangular with respect equilateral equilateral polygon equivalent frustum given angle given circle given line given point given polygon given sides given square gles greater half the product Hence homologous sides hypothenuse included angle infinite number Inscribed Angle Join AC Let ABCD line AB fig line BC mean proportional measure half number of sides oblique lines parallel lines parallel to BC parallelogram parallelopiped perimeter perpendicular point A fig polyedron polygon ABCD &c preceding prism Problem Proof radii rectangle regular polygon respectively equal rhombus right triangles Scholium secant segment side AC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle tangent Theorem triangles ABC vertex vertices

### 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 viii - A line parallel to one side of a triangle divides the other two sides proportionally.

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 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 16 - Theorem. In an isosceles triangle the angles opposite the equal sides are equal.

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 136 - ADC ; the last two are therefore right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular to the base, and bisects the vertical angle.

Page 122 - The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and a mean proportional between the bases of the frustum.

Page xviii - In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.