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 sider |
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Side 49
... compared together are called the terms of the propor tion . The first and last terms are called the two extremes , and the second and third terms , the two means . 7. Of four proportional quantities , the last is said 4 BOOK II . 49.
... compared together are called the terms of the propor tion . The first and last terms are called the two extremes , and the second and third terms , the two means . 7. Of four proportional quantities , the last is said 4 BOOK II . 49.
Side 51
... extremes is equal to the product of the two means . Let A , B , C , D , be any four magnitudes , and M , N , P , 2 , their numerical representatives ; then , if M N P Q M : NP Q , we shall have MxQ = NxP . For , since the magnitudes are ...
... extremes is equal to the product of the two means . Let A , B , C , D , be any four magnitudes , and M , N , P , 2 , their numerical representatives ; then , if M N P Q M : NP Q , we shall have MxQ = NxP . For , since the magnitudes are ...
Side 52
... extremes , and N and a proportion ( P. 2 ) ; For , since M therefore M and P the means of hence , M : P :: N : Q. PROPOSITION IV . THEOREM . If there be four proportional magnitudes , and four other pro- portional magnitudes , having ...
... extremes , and N and a proportion ( P. 2 ) ; For , since M therefore M and P the means of hence , M : P :: N : Q. PROPOSITION IV . THEOREM . If there be four proportional magnitudes , and four other pro- portional magnitudes , having ...
Side 53
... extremes , and M and Q the means of a proportion ( P. 2 ) : hence N : M :: Q : P. PROPOSITION VI . THEOREM . If four magnitudes are in proportion , they will be in propor tion by composition or division . If we have M : N :: P : Q , we ...
... extremes , and M and Q the means of a proportion ( P. 2 ) : hence N : M :: Q : P. PROPOSITION VI . THEOREM . If four magnitudes are in proportion , they will be in propor tion by composition or division . If we have M : N :: P : Q , we ...
Side 54
... 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 consequents be either augmented or diminished by magnitudes which have ...
... 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 consequents be either augmented or diminished by magnitudes which have ...
Andre utgaver - Vis alle
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... Adrien Marie Legendre,Charles Davies Uten tilgangsbegrensning - 1890 |
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... Charles Davies Uten tilgangsbegrensning - 1874 |
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... Adrien Marie Legendre,Charles Davies Uten tilgangsbegrensning - 1864 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Side 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...
Side 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Side 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.
Side 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.
Side 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'.
Side 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.
Side 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Side 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.
Side 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.