Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1854 - 432 páginas |
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Página 87
... equivalent , denotes an equality in one respect only ; viz .: an equality between the measures of figures . The sign , denotes equivalency , and is read , is equivalent to . 5. Two sides of one figure are said to be reciprocally ...
... equivalent , denotes an equality in one respect only ; viz .: an equality between the measures of figures . The sign , denotes equivalency , and is read , is equivalent to . 5. Two sides of one figure are said to be reciprocally ...
Página 88
... equivalent . Since the two parallelograms have equal bases , those bases may be placed the one on the other . Therefore , let AB be the common base of the two parallelograms ABCD , ABEF , which have the same altitude : then will they be ...
... equivalent . Since the two parallelograms have equal bases , those bases may be placed the one on the other . Therefore , let AB be the common base of the two parallelograms ABCD , ABEF , which have the same altitude : then will they be ...
Página 89
... equivalent . Scholium . Since the rectangle and square are parallelo- grams ( B. I. , D. 25 ) , it follows that either is equivalent to any parallelogram having an equal base and an equal altitude . And generally , whatever property is ...
... equivalent . Scholium . Since the rectangle and square are parallelo- grams ( B. I. , D. 25 ) , it follows that either is equivalent to any parallelogram having an equal base and an equal altitude . And generally , whatever property is ...
Página 94
... equivalent to the parallelogram ALKD , and consequently , is measured by EFXAL ( P. 5 ) . But we have AL = DK ; and since the triangles IBL and KCI are equal , the side BL = CK : hence AB + CD = AL + DK = 2AL ; hence , AL is the half ...
... equivalent to the parallelogram ALKD , and consequently , is measured by EFXAL ( P. 5 ) . But we have AL = DK ; and since the triangles IBL and KCI are equal , the side BL = CK : hence AB + CD = AL + DK = 2AL ; hence , AL is the half ...
Página 95
... equivalent to the sum of the squares described on the lines , together with twice the rectangle contained by the lines . Let AB , BC , be any two lines , and AC their sum ; then F E H D I G AC2 or ( AB + BC ) 2 ~ AB2 + BC2 + 2AB × BC ...
... equivalent to the sum of the squares described on the lines , together with twice the rectangle contained by the lines . Let AB , BC , be any two lines , and AC their sum ; then F E H D I G AC2 or ( AB + BC ) 2 ~ AB2 + BC2 + 2AB × BC ...
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Términos y frases comunes
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices
Pasajes populares
Página 27 - If two triangles have two sides of the one equal to two sides of the...
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Página 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Página 26 - The sum of any two sides of a triangle is greater than the third side.
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 93 - The area of a parallelogram is equal to the product of its base and altitude.
Página 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Página 323 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Página 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.