An Elementary Treatise on Plane and Solid GeometryJ. Munroe and Company, 1847 - 150 σελίδες |
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Σελίδα iv
... greater than the greatest possible error which could be obtained , a manifest absurdity , but one which cannot be avoided as long as A is any thing . The term direction is introduced into this trea- tise without being defined ; but it ...
... greater than the greatest possible error which could be obtained , a manifest absurdity , but one which cannot be avoided as long as A is any thing . The term direction is introduced into this trea- tise without being defined ; but it ...
Σελίδα vi
... Greater side of a triangle opposite the greater angle ( 62 ) , Case of equal right triangles ( 64 ) , · Sum of the angles of a triangle ( 65–71 ) , • 14 14 5367 15 • · 15 • 16 • 17 • 17 18 · 20 20 122 773 22 23 23 23 23 23 24 · · គន ...
... Greater side of a triangle opposite the greater angle ( 62 ) , Case of equal right triangles ( 64 ) , · Sum of the angles of a triangle ( 65–71 ) , • 14 14 5367 15 • · 15 • 16 • 17 • 17 18 · 20 20 122 773 22 23 23 23 23 23 24 · · គន ...
Σελίδα xii
... greater than the third • Sum of plane angles of a solid angle ( 339 ) , 103 103 104 104 • 105 · Solid angles formed by equal plane angles ( 340 ) , 106 · CHAPTER XVI . SURFACE AND SOLIDITY OF SOLIDS , · 107 107 107 Equivalent solids ...
... greater than the third • Sum of plane angles of a solid angle ( 339 ) , 103 103 104 104 • 105 · Solid angles formed by equal plane angles ( 340 ) , 106 · CHAPTER XVI . SURFACE AND SOLIDITY OF SOLIDS , · 107 107 107 Equivalent solids ...
Σελίδα xiii
... greater than difference between two right angles and sum of the other two angles ( 448 ) , Case of equal or symmetrical spherical triangles ( 449 - 452 , 458 ) , 134 Equal sides and angles of isosceles or equilateral spherical tri ...
... greater than difference between two right angles and sum of the other two angles ( 448 ) , Case of equal or symmetrical spherical triangles ( 449 - 452 , 458 ) , 134 Equal sides and angles of isosceles or equilateral spherical tri ...
Σελίδα xv
... greater than . Thus , A > B is A greater than B. The sign is less than . Thus , A < B is A less than B. A2 indicates the second power of A , A3 the third power , & c . A ratio or fraction is the quotient of one quantity divid- ed by ...
... greater than . Thus , A > B is A greater than B. The sign is less than . Thus , A < B is A less than B. A2 indicates the second power of A , A3 the third power , & c . A ratio or fraction is the quotient of one quantity divid- ed by ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 20 - The sum of the three angles of any triangle is equal to two right angles.
Σελίδα xv - The first term of a ratio is called the antecedent, and the second term the consequent.
Σελίδα 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...
Σελίδα 31 - Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords.
Σελίδα 87 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Σελίδα 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.
Σελίδα 78 - Similar triangles are to each other as the squares of their homologous sides. Proof. In the similar .triangles ABC, A'B'C