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 58
... be inscribed in the poly- gon . POSTULATE . 12. Let it be granted that the circumference of a circle . may be described from any centre , and with any radius . PROPOSITION I. THEOREM . Every diameter divides the circle and 58 GEOMETRY .
... be inscribed in the poly- gon . POSTULATE . 12. Let it be granted that the circumference of a circle . may be described from any centre , and with any radius . PROPOSITION I. THEOREM . Every diameter divides the circle and 58 GEOMETRY .
Página 63
... described from the centre 0 , with the radius OB , will pass through the three given points , A , B , C. We have now shown that one circumference can always be nade to pass through three given points , not in the same straight line : we ...
... described from the centre 0 , with the radius OB , will pass through the three given points , A , B , C. We have now shown that one circumference can always be nade to pass through three given points , not in the same straight line : we ...
Página 66
... joining the centres , and at equal distances from it . Let the two circumferences described about the centres and D intersect each other at the point A ; draw AF perpendicular to CD , and prolong it till BF is 66 GEOMETRY .
... joining the centres , and at equal distances from it . Let the two circumferences described about the centres and D intersect each other at the point A ; draw AF perpendicular to CD , and prolong it till BF is 66 GEOMETRY .
Página 67
... described about the centre C , with the radius CA , will pass through B. In the same manner it may be shown , that the circumfer- ence described about the centre D , with the radius DA , will also pass through B. Cor . If two ...
... described about the centre C , with the radius CA , will pass through B. In the same manner it may be shown , that the circumfer- ence described about the centre D , with the radius DA , will also pass through B. Cor . If two ...
Página 72
... described with equal radii . Scholium 2. An angle less than a right angle will be measured by an arc less than a quarter of the circumfer ence : a right angle , by a quarter of the circumference : and an obtuse angle by an arc greater ...
... described with equal radii . Scholium 2. An angle less than a right angle will be measured by an arc less than a quarter of the circumfer ence : a right angle , by a quarter of the circumference : and an obtuse angle by an arc greater ...
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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.