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 iv
... inscribed and circumscribed polygons , the demonstrations in Book V. have been much simplified ; and the same principle is made the basis of several im- portant demonstrations in Book VIII . The subjects of Plane and Spherical ...
... inscribed and circumscribed polygons , the demonstrations in Book V. have been much simplified ; and the same principle is made the basis of several im- portant demonstrations in Book VIII . The subjects of Plane and Spherical ...
Página 57
... two arcs , and consequently , also to two segments : but the smaller one is always meant , unless the contrary is expressed . 6. A STRAIGHT LINE is said to be inscribed in BOOK III The Circle, and the Measurement of Angles,.........
... two arcs , and consequently , also to two segments : but the smaller one is always meant , unless the contrary is expressed . 6. A STRAIGHT LINE is said to be inscribed in BOOK III The Circle, and the Measurement of Angles,.........
Página 58
... inscribed in a circle , when its extremities are in the circumference . An inscribed angle is one which has its vertex in the circumference , and is included by two chords of the circle . 7. An inscribed triangle is one which has the ...
... inscribed in a circle , when its extremities are in the circumference . An inscribed angle is one which has its vertex in the circumference , and is included by two chords of the circle . 7. An inscribed triangle is one which has the ...
Página 59
... inscribed in a circle is a diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those three points would be equally distant from ...
... inscribed in a circle is a diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those three points would be equally distant from ...
Página 73
... inscribed angle is measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first sup pose the centre of the circle to lie within the angle BAD . Draw the diameter ACE , and the radii CB , CD ...
... inscribed angle is measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first sup pose the centre of the circle to lie within the angle BAD . Draw the diameter ACE , and the radii CB , CD ...
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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.