An Elementary Treatise on Plane and Solid GeometryJ. Munroe and Company, 1847 - 150 σελίδες |
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Σελίδα vi
... equiangular polygon ( 49 ) ; polygons equilateral and equiangular with respect to each other , and their homolo- gous sides and angles ( 50 ) , Three cases of equal triangles ( 51 , 53 , 61 ) , Equal sides and angles of the isosceles ...
... equiangular polygon ( 49 ) ; polygons equilateral and equiangular with respect to each other , and their homolo- gous sides and angles ( 50 ) , Three cases of equal triangles ( 51 , 53 , 61 ) , Equal sides and angles of the isosceles ...
Σελίδα 15
... equiangular polygon is one which has all its angles equal . 50. Definition . Two polygons are equilateral with respect to each other , when they have their sides equal , each to each , and placed in the same order ; that is , when , by ...
... equiangular polygon is one which has all its angles equal . 50. Definition . Two polygons are equilateral with respect to each other , when they have their sides equal , each to each , and placed in the same order ; that is , when , by ...
Σελίδα 17
... equi- angular . 57. Theorem . The line BD ( fig . 32 ) , which bi- sects the angle B , at the vertex of an isosceles ... equiangular triangle is also equi- lateral . 60. Lemma . Third Case of Equal Triangles . Two CH . VII . § 59. ] 17 ...
... equi- angular . 57. Theorem . The line BD ( fig . 32 ) , which bi- sects the angle B , at the vertex of an isosceles ... equiangular triangle is also equi- lateral . 60. Lemma . Third Case of Equal Triangles . Two CH . VII . § 59. ] 17 ...
Σελίδα 18
... equiangular with respect to each other . Proof . Let ABC and DEF ( fig . 31 ) be the triangles , whose sides AB , BC , and AC are respectively equal to DE , EF , and DF . If DE is placed upon AB , the point F must by the preceding ...
... equiangular with respect to each other . Proof . Let ABC and DEF ( fig . 31 ) be the triangles , whose sides AB , BC , and AC are respectively equal to DE , EF , and DF . If DE is placed upon AB , the point F must by the preceding ...
Σελίδα 21
... equiangular with respect to each other . 68. Corollary . In a triangle , there can only be one right angle , or one obtuse angle . 69. Corollary . In a right triangle , the sum of the acute angles is equal to a right angle . 70 ...
... equiangular with respect to each other . 68. Corollary . In a triangle , there can only be one right angle , or one obtuse angle . 69. Corollary . In a right triangle , the sum of the acute angles is equal to a right angle . 70 ...
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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