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 ii
... EQUATIONS OF THE POINT AND STRAIGHT LINE - of the CONIC SECTIONS - of the LINE AND PLANE IN SPACE ; also , the discussion of the GENERAL EQUATION of the second degree , and of SUR- FACES of the second order . Davies ' Differential And ...
... EQUATIONS OF THE POINT AND STRAIGHT LINE - of the CONIC SECTIONS - of the LINE AND PLANE IN SPACE ; also , the discussion of the GENERAL EQUATION of the second degree , and of SUR- FACES of the second order . Davies ' Differential And ...
Página 52
... equations member by member , MXQXRXP = M × S × N × P ; cancelling MXP in both members , we have , QXR - SXN : hence ( P. 2 ) , N Q R S :: : Cor . If there be two sets of proportionals , in which the ratio of an antecedent and consequent ...
... equations member by member , MXQXRXP = M × S × N × P ; cancelling MXP in both members , we have , QXR - SXN : hence ( P. 2 ) , N Q R S :: : Cor . If there be two sets of proportionals , in which the ratio of an antecedent and consequent ...
Página 53
... equation to , and subtract it from MXP , and we shall have , MXP ± NXP = M × P ± M × Q ; or ( M ± N ) × P = ( P ± Q ) × M . But M ± N and P , may be considered the two extremes , and PQ and M , the two means of a proportion ( P. 2 ) ...
... equation to , and subtract it from MXP , and we shall have , MXP ± NXP = M × P ± M × Q ; or ( M ± N ) × P = ( P ± Q ) × M . But M ± N and P , may be considered the two extremes , and PQ and M , the two means of a proportion ( P. 2 ) ...
Página 54
... equation by m × n . But m XM and n XQ , may be regarded as the two extremes , and n X N and mXP , as the means of a proportion ; hence , mxM : nxN :: mxP : nx Q. PROPOSITION IX . THEOREM . Of four proportional magnitudes , if the two ...
... equation by m × n . But m XM and n XQ , may be regarded as the two extremes , and n X N and mXP , as the means of a proportion ; hence , mxM : nxN :: mxP : nx Q. PROPOSITION IX . THEOREM . Of four proportional magnitudes , if the two ...
Página 249
... equations of the problem . The solution of these equations , when so formed , gives the solution of the problem . No general rule can be given for forming the equations . The equations must be independent of each other , and their ...
... equations of the problem . The solution of these equations , when so formed , gives the solution of the problem . No general rule can be given for forming the equations . The equations must be independent of each other , and their ...
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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.