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 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 straight 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 straight 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 , AC 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 , AC 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 ...
... 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 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 27 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Σελίδα 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.
Σελίδα 26 - The sum of any two sides of a triangle is greater than the third side.
Σελίδα 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Σελίδα 93 - The area of a parallelogram is equal to the product of its base and altitude.
Σελίδα 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Σελίδα 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.
Σελίδα 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.