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 19
... whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10 All right angles are equal to each other . BOOK I. 19.
... whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10 All right angles are equal to each other . BOOK I. 19.
Σελίδα 20
... whole extent , are equal POSTULATES . 1. Let it be granted , that a straight line may be drawn from one point to another point . 2. That a terminated straight line may be prolonged , in a straight line , to any length . 3. That if two ...
... whole extent , are equal POSTULATES . 1. Let it be granted , that a straight line may be drawn from one point to another point . 2. That a terminated straight line may be prolonged , in a straight line , to any length . 3. That if two ...
Σελίδα 22
... whole extent , and form one and the same straight line . Let A and B be the two common points of two straigh lines . In the first place , the two lines will coincide between the points A and B ; for , otherwise there would be two ...
... whole extent , and form one and the same straight line . Let A and B be the two common points of two straigh lines . In the first place , the two lines will coincide between the points A and B ; for , otherwise there would be two ...
Σελίδα 23
... whole equal to a part , which is impossible ( A. 8 ) : therefore , A and CB form one and the same straight line . PROPOSITION IV . THEOREM . When two straight lines intersect each other , the opposite or vertical angles , which they ...
... whole equal to a part , which is impossible ( A. 8 ) : therefore , A and CB form one and the same straight line . PROPOSITION IV . THEOREM . When two straight lines intersect each other , the opposite or vertical angles , which they ...
Σελίδα 30
... whole ( A. 8 ) ; hence , there is no inequality between the sides BA and AC ; therefore , the triangle BAC is isosceles . PROPOSITION XIII . THEOREM . The greater side of every triangle is opposite to the greater angle ; and conversely ...
... whole ( A. 8 ) ; hence , there is no inequality between the sides BA and AC ; therefore , the triangle BAC is isosceles . PROPOSITION XIII . THEOREM . The greater side of every triangle is opposite to the greater angle ; and conversely ...
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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.