Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Page 14
... to be perpendicu lar to the second . 14. An ACUTE ANGLE is an angle ess than a right angle . 15. An OBTUSE ANGLE is an angle greater than a right angle . 16. Two straight lines are said to be parallel , 14 GEOMETRY .
... to be perpendicu lar to the second . 14. An ACUTE ANGLE is an angle ess than a right angle . 15. An OBTUSE ANGLE is an angle greater than a right angle . 16. Two straight lines are said to be parallel , 14 GEOMETRY .
Page 18
... greater than B , the expression A > B is used ; the smaller quantity being always at the vertex of the angle . 4. The sign is called plus ; it indicates addition . 5. The sign is called minus ; it indicates subtraction : Thus , A + B ...
... greater than B , the expression A > B is used ; the smaller quantity being always at the vertex of the angle . 4. The sign is called plus ; it indicates addition . 5. The sign is called minus ; it indicates subtraction : Thus , A + B ...
Page 19
... . Things which are halves of equal things , are equal to each other . 8. The 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.
... . Things which are halves of equal things , are equal to each other . 8. The 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.
Page 20
... greater . 4. That a given straight line may be bisected : that is , divided into two equal parts . 5. That a straight line may bisect a given angle . 6. That a perpendicular may be drawn to a given straight line , either from a point ...
... greater . 4. That a given straight line may be bisected : that is , divided into two equal parts . 5. That a straight line may bisect a given angle . 6. That a perpendicular may be drawn to a given straight line , either from a point ...
Page 26
... greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AB , BC , be greater than the third side AC For the straight line AC is the short- est distance between the points A and C ( A. 12 ) ...
... greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AB , BC , be greater than the third side AC For the straight line AC is the short- est distance between the points A and C ( A. 12 ) ...
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Common terms and phrases
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
Popular passages
Page 27 - If two triangles have two sides of the one equal to two sides of the...
Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 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.
Page 26 - The sum of any two sides of a triangle is greater than the third side.
Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 93 - The area of a parallelogram is equal to the product of its base and altitude.
Page 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 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.
Page 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.