An Elementary Treatise on Plane and Solid GeometryJ. Munroe and Company, 1847 - 150 σελίδες |
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Σελίδα xvii
... & c . If both the means of the proportion are of the same magnitude , this mean is called the mean proportional be- tween the extremes . Thus , if A : B B : D , = B is a mean proportional ... A B C D = & c . EXPLANATION OF SIGNS , & c . xvii.
... & c . If both the means of the proportion are of the same magnitude , this mean is called the mean proportional be- tween the extremes . Thus , if A : B B : D , = B is a mean proportional ... A B C D = & c . EXPLANATION OF SIGNS , & c . xvii.
Σελίδα xviii
Benjamin Peirce. M whence A B C D = & c . ; : A = : BX M , C = DX M , EFX M , & c . = and the sum of these equations is A + C + E + & c . = ( B + D + F + & c . ) × M ; whence A + C ÷ E + & c . B + D + F + & c . - M = - A C B D = & c ...
Benjamin Peirce. M whence A B C D = & c . ; : A = : BX M , C = DX M , EFX M , & c . = and the sum of these equations is A + C + E + & c . = ( B + D + F + & c . ) × M ; whence A + C ÷ E + & c . B + D + F + & c . - M = - A C B D = & c ...
Σελίδα 56
... ABCD , & c . , A'B'C ' D ' , & c . ( fig . 108 ) are composed of the same number of triangles ABC , ACD , & c . , A'B'C ' , A'C'D ' , & c . which are similar each to each and similarly dis- posed , the polygons are similar . Proof ...
... ABCD , & c . , A'B'C ' D ' , & c . ( fig . 108 ) are composed of the same number of triangles ABC , ACD , & c . , A'B'C ' , A'C'D ' , & c . which are similar each to each and similarly dis- posed , the polygons are similar . Proof ...
Σελίδα 57
... C ' , ACD , & c . are similar to ABC , ACD , & c . each to each , and therefore , by the preceding theorem , the polygons are similar . 195. Theorem . If the similar polygons ABCD & c . ABC'D ' & c . ( fig . 109 ) have a side AB of the ...
... C ' , ACD , & c . are similar to ABC , ACD , & c . each to each , and therefore , by the preceding theorem , the polygons are similar . 195. Theorem . If the similar polygons ABCD & c . ABC'D ' & c . ( fig . 109 ) have a side AB of the ...
Σελίδα 58
... ABCD & c . 197. Theorem . The perimeters of similar polygons are as their homologous sides . Proof . From the definition of § 170 , the similar poly- gons ABCD & c . ( fig . 108 ) , A'B'C'D ' & c . give the pro- portion AB : A'B ' — BC : B' ...
... ABCD & c . 197. Theorem . The perimeters of similar polygons are as their homologous sides . Proof . From the definition of § 170 , the similar poly- gons ABCD & c . ( fig . 108 ) , A'B'C'D ' & c . give the pro- portion AB : A'B ' — BC : B' ...
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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