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 88
... altitude of a trapezoid is the perpendicular distance between its two parallel sides . B A D E C G F PROPOSITION I. THEOREM . Parallelograms which have equal bases and equal altitudes , are equivalent . Since the two parallelograms have ...
... altitude of a trapezoid is the perpendicular distance between its two parallel sides . B A D E C G F PROPOSITION I. THEOREM . Parallelograms which have equal bases and equal altitudes , are equivalent . Since the two parallelograms have ...
Página 89
... altitudes , are 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 ...
... altitudes , are 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 ...
Página 90
... altitudes are to each other as their bases . Let ABCD , AEFD , be two rectangles having the com mon altitude AD : they are to each other as their bases AB , AE . D A F C E B First . Suppose that the bases are commensurable , and are to ...
... altitudes are to each other as their bases . Let ABCD , AEFD , be two rectangles having the com mon altitude AD : they are to each other as their bases AB , AE . D A F C E B First . Suppose that the bases are commensurable , and are to ...
Página 91
... altitudes , are to each other as their bases . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the ... altitude AE , are to each other as their bases AD , AF thus we have , : ABCD : AEHD :: AB AE , AEHD AEGF : :: AD ...
... altitudes , are to each other as their bases . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the ... altitude AE , are to each other as their bases AD , AF thus we have , : ABCD : AEHD :: AB AE , AEHD AEGF : :: AD ...
Página 92
... altitude : then , the product of these two ratios may be assumed as the measure of the rectangle . 3 2 A 1 2 3 4 5 6 7 8 9 10 For example , if the base of the rectangle A contains ten units and its altitude three , the rectangle will be ...
... altitude : then , the product of these two ratios may be assumed as the measure of the rectangle . 3 2 A 1 2 3 4 5 6 7 8 9 10 For example , if the base of the rectangle A contains ten units and its altitude three , the rectangle will be ...
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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.