Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 11
... greater quantity . The sign , .. is used as an abbreviation of the word hence , or consequently . 5. The general truths of Geometry are deduced by a course of logical reasoning , the premises being definitions and principles previously ...
... greater quantity . The sign , .. is used as an abbreviation of the word hence , or consequently . 5. The general truths of Geometry are deduced by a course of logical reasoning , the premises being definitions and principles previously ...
Page 14
... the adjacent angles unequal . D B Oblique angles are subdivided into two classes , acute angles , and obtuse angles . 14. An ACUTE ANGLE is less than a right angle Kollin 15. An OBTUSE ANGLE is greater than a right 14 GEOMETRY .
... the adjacent angles unequal . D B Oblique angles are subdivided into two classes , acute angles , and obtuse angles . 14. An ACUTE ANGLE is less than a right angle Kollin 15. An OBTUSE ANGLE is greater than a right 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 between two points . 12. The shortest distance between any two points is mea ...
... 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 between two points . 12. The shortest distance between any two points is mea ...
Page 26
... greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side For , the distance from A AC . 2 to C , measured on any broken line AB , BC , A is greater than the ...
... greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side For , the distance from A AC . 2 to C , measured on any broken line AB , BC , A is greater than the ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following