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 σελίδες |
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Σελίδα 58
... be inscribed in the poly- gon . ооо 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 . ооо 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 .
Σελίδα 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 made to pass through three given points , not in the sa.ne straight line ...
... 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 made to pass through three given points , not in the sa.ne straight line ...
Σελίδα 66
... joining the centres , and at equal distances from it . Let the two circumferences described about the centres C 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 C and D intersect each other at the point A ; draw AF perpendicular to CD , and prolong it till BF is 66 GEOMETRY .
Σελίδα 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 ...
Σελίδα 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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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 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...
Σελίδα 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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'.
Σελίδα 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.
Σελίδα 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Σελίδα 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.
Σελίδα 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.