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, 1857 - 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 Sun- FACES of the second order . Babies ' 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 Sun- FACES of the second order . Babies ' Differential and ...
Página 52
... equations member by member , MXQXRXP = M × S × N × P ; cancelling MXP in both members , we have , QXR = S × N : hence ( P. 2 ) , N Q R S Cor . If there be two sets of proportionals , in which the ratio of an antecedent and consequent of ...
... equations member by member , MXQXRXP = M × S × N × P ; cancelling MXP in both members , we have , QXR = S × N : hence ( P. 2 ) , N Q R S Cor . If there be two sets of proportionals , in which the ratio of an antecedent and consequent of ...
Página 53
... equation to , and subtract it from MXP , and we shall have , MXP ± NXP MXP ± MXQ ; 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 ) : hence ...
... equation to , and subtract it from MXP , and we shall have , MXP ± NXP MXP ± MXQ ; 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 ) : hence ...
Página 54
... equation by mxn . But m XM and n X Q , 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 mxn . But m XM and n X Q , 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
altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cos² cosine Cotang cubes 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 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 similar triangles sin² sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM three angles triangle ABC triangular prism triedral angles vertex vertices
Pasajes populares
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 34 - If two right-angled triangles have the hypothenuse and a side of the one, equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 278 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Página 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página 1 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.
Página 43 - BtSL hence the sum of all the interior and exterior angles, is equal to twice as many right angles as the polygon has sides.
Página 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Página 30 - B : hence the two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each : hence, the two triangles are equal (Th.
Página 97 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.