An Elementary Treatise on Plane and Solid Geometry |
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Page vii
... formed by tangent and chord ( 121 ) , Measure of angle formed by two secants , two tangents , or a tangent and secant ( 122 ) ; of angle formed by two chords ( 123 ) , Arcs intercepted by parallels ( 124 ) , Line joining the centres of ...
... formed by tangent and chord ( 121 ) , Measure of angle formed by two secants , two tangents , or a tangent and secant ( 122 ) ; of angle formed by two chords ( 123 ) , Arcs intercepted by parallels ( 124 ) , Line joining the centres of ...
Page xi
... formed with two given sides ( 305 ) , Maximum of polygons formed with sides all given but one ( 306 ) , 92 Maximum of polygons formed with given sides ( 307 ) , Greatest of isoperimetrical regular polygons ( 309 ) , Maximum of ...
... formed with two given sides ( 305 ) , Maximum of polygons formed with sides all given but one ( 306 ) , 92 Maximum of polygons formed with given sides ( 307 ) , Greatest of isoperimetrical regular polygons ( 309 ) , Maximum of ...
Page xii
... formed by equal plane angles ( 340 ) , 106 · CHAPTER XVI . SURFACE AND SOLIDITY OF SOLIDS , · 107 107 107 Equivalent solids ( 341 ) ; lamina ( 341 ) , Case in which solids are equivalent ( 342 ) , Polyedron , and its faces and sides ...
... formed by equal plane angles ( 340 ) , 106 · CHAPTER XVI . SURFACE AND SOLIDITY OF SOLIDS , · 107 107 107 Equivalent solids ( 341 ) ; lamina ( 341 ) , Case in which solids are equivalent ( 342 ) , Polyedron , and its faces and sides ...
Page xvi
... formed by two equal ratios . Thus , if the two ratios A : B and C : D are equal , the equation A : B = C : D is a proportion , and it may also be written - A C B D The first and last terms of a proportion are called its extremes ; and ...
... formed by two equal ratios . Thus , if the two ratios A : B and C : D are equal , the equation A : B = C : D is a proportion , and it may also be written - A C B D The first and last terms of a proportion are called its extremes ; and ...
Page 6
... formed by two lines meeting or crossing each other . The Vertex of the angle is the point where its sides meet . The magnitude of the angle depends solely upon the difference of direction of its sides at the vertex . a . The magnitude ...
... formed by two lines meeting or crossing each other . The Vertex of the angle is the point where its sides meet . The magnitude of the angle depends solely upon the difference of direction of its sides at the vertex . a . The magnitude ...
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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 construct convex surface Corollary 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 sides given square gles greater half the product Hence homologous sides hypothenuse infinite number infinitely small Inscribed Angle inscribed circle isosceles Let ABCD line AB fig line BC lines drawn 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 sector segment side BC similar polygons similar triangles solid angle Solution sphere spherical polygon spherical triangle straight line tangent Theorem triangles ABC triangular prism 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