An Elementary Treatise on Plane and Solid GeometryJ. Munroe and Company, 1847 - 150 σελίδες |
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Αποτελέσματα 1 - 5 από τα 43.
Σελίδα vii
... radius and diame . ter ( 86 ) , • · · Comparative magnitude of radii and diameters ( 87 ) , Circle bisected by the diameter ( 88 ) ; semicircumference and semicircle ( 89 ) ; arc and its chord ( 90 ) , Chord less than diameter ( 91 ) ...
... radius and diame . ter ( 86 ) , • · · Comparative magnitude of radii and diameters ( 87 ) , Circle bisected by the diameter ( 88 ) ; semicircumference and semicircle ( 89 ) ; arc and its chord ( 90 ) , Chord less than diameter ( 91 ) ...
Σελίδα xiii
... radius and diameter ( 417 , 418 ) , · • Section of sphere ( 419 ) ; great and small circles ( 420–422 ) , Pole of circle ( 423 ) ; distance of pole from circumference ( 424 , 425 ) , Arcs drawn on surface of sphere ( 426 ) , Case in ...
... radius and diameter ( 417 , 418 ) , · • Section of sphere ( 419 ) ; great and small circles ( 420–422 ) , Pole of circle ( 423 ) ; distance of pole from circumference ( 424 , 425 ) , Arcs drawn on surface of sphere ( 426 ) , Case in ...
Σελίδα 23
... and AD ; and therefore AB and CD must be equal and parallel . 82. Theorem . Two parallel lines are throughout at the same distance from each other . The Circle , Radius . Proof . The two parallels 2 * CH . VII . § 82. ] 23 POLYGONS .
... and AD ; and therefore AB and CD must be equal and parallel . 82. Theorem . Two parallel lines are throughout at the same distance from each other . The Circle , Radius . Proof . The two parallels 2 * CH . VII . § 82. ] 23 POLYGONS .
Σελίδα 24
Benjamin Peirce. The Circle , Radius . Proof . The two parallels AB and CD ( fig . 40 ) , being given , if through two ... radius of a circle is the straight Diameter , Inscribed Lines . line , as AB , 24 PLANE GEOMETRY . [ CH . VIII . § 86 .
Benjamin Peirce. The Circle , Radius . Proof . The two parallels AB and CD ( fig . 40 ) , being given , if through two ... radius of a circle is the straight Diameter , Inscribed Lines . line , as AB , 24 PLANE GEOMETRY . [ CH . VIII . § 86 .
Σελίδα 25
... radius . 88. Theorem . Every diameter , as BD ( fig . 43 ) , bi- sects the circle and its circumference . Proof . For if the figure BCD be folded over upon the part BED , they must coincide ; otherwise there would be points in the one ...
... radius . 88. Theorem . Every diameter , as BD ( fig . 43 ) , bi- sects the circle and its circumference . Proof . For if the figure BCD be folded over upon the part BED , they must coincide ; otherwise there would be points in the one ...
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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