An Elementary Treatise on Plane and Solid Geometry |
Other editions - View all
Common terms and phrases
ABC fig altitude angle BAC arc BC base and altitude bisect centre circumference circumscribed coincide construct Corollary 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 ratio given sides given square greater half the product Hence homologous sides hypothenuse infinite number Inscribed Angle inscribed circle isosceles Join AC line AB fig mean proportional measure half number of sides parallel lines parallel to BC parallelogram parallelopipeds perimeter perpendicular plane point of division polyedron polygon ABCD &c preceding prism Problem Proof pyramid radii rectangle regular polygon right triangle Scholium secant sector semicircle side BC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle tangent Theorem trapezoid triangle ABC triangles are similar vertex vertices whence
Popular passages
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 127 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.
Page 71 - 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 20 - The sum of the three angles of any triangle is equal to two right angles.
Page xv - The first term of a ratio is called the antecedent, and the second term the consequent.
Page 83 - ... 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 squares of their radii. Proof. The similar sectors AOB, A'OB ' (fig. 136) are, by the same reasoning as in t5 97, the same parts of their respective circles, which the angle O= O...
Page 31 - Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords.
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 99 - B, from the plane. 320. Theorem. Oblique lines drawn from a point to a plane at equal distances from the perpendicular are equal; and of two oblique lines unequally distant the more remote is the greater.
Page 78 - Similar triangles are to each other as the squares of their homologous sides. Proof. In the similar .triangles ABC, A'B'C