Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page iv
... greater clearness of expression or of proof , as could be made with- out altering it in form or substance . Practical exercises have been placed at the end of the several books , and comprise additional theorems , problems , and ...
... greater clearness of expression or of proof , as could be made with- out altering it in form or substance . Practical exercises have been placed at the end of the several books , and comprise additional theorems , problems , and ...
Page 11
... greater quantity . The sign , ... is used as an abbreviation of the word hence , or consequently . The symbols , 1o , 2o , etc. , mean 1st , 2d , etc. 5. The general truths of Geometry are deduced by a course of logical reasoning , the ...
... greater quantity . The sign , ... is used as an abbreviation of the word hence , or consequently . The symbols , 1o , 2o , etc. , mean 1st , 2d , etc. 5. The general truths of Geometry are deduced by a course of logical reasoning , the ...
Page 14
... make the adjacent angles unequal . Oblique angles are subdivided into two classes , acute angles , and obtuse angles . 14. An ACUTE ANGLE is less than a right angle . 15. An OBTUSE ANGLE is greater than a right angle 14 GEOMETRY .
... make the adjacent angles unequal . Oblique angles are subdivided into two classes , acute angles , and obtuse angles . 14. An ACUTE ANGLE is less than a right angle . 15. An OBTUSE ANGLE is greater than a right angle 14 GEOMETRY .
Page 15
... greater than a right angle . 16. Two straight lines are parallel , when they lie in the same plane and can not meet , how far soever , either way , both may be produced . They then have the same direction . 17. A PLANE FIGURE is a ...
... greater than a right angle . 16. Two straight lines are parallel , when they lie in the same plane and can not meet , how far soever , either way , both may be produced . They then have the same direction . 17. A PLANE FIGURE is a ...
Page 18
... greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. All right angles are equal . 11. Only one straight line can be drawn joining two given points . 12. The shortest distance from one point to another ...
... greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. All right angles are equal . 11. Only one straight line can be drawn joining two given points . 12. The shortest distance from one point to another ...
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence