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 v
... Problems relating to the First and Third Books ,. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , 82 6899 59 93 129 136 BOOK VI ...
... Problems relating to the First and Third Books ,. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , 82 6899 59 93 129 136 BOOK VI ...
Page vi
... Problems of Application , PAGE . 210 TRIGONOMETRY . ANALYTICAL Analytical Trigonometry Defined , Definitions and General Principles , .. Rules for Signs of the Functions ,. 235 34 5 7 8 11 12 13 15 16 17 18-22 22 22 23-27 27-35 36-47 48 ...
... Problems of Application , PAGE . 210 TRIGONOMETRY . ANALYTICAL Analytical Trigonometry Defined , Definitions and General Principles , .. Rules for Signs of the Functions ,. 235 34 5 7 8 11 12 13 15 16 17 18-22 22 22 23-27 27-35 36-47 48 ...
Page 11
... PROBLEM is a question requiring a solution . 9. A POSTULATE is a problem whose solution is self- evident . Theorems , Axioms , Problems , and Postulates , are all called Propositions . 10. A LEMMA is an auxiliary proposition . 11. A ...
... PROBLEM is a question requiring a solution . 9. A POSTULATE is a problem whose solution is self- evident . Theorems , Axioms , Problems , and Postulates , are all called Propositions . 10. A LEMMA is an auxiliary proposition . 11. A ...
Page 19
... Problem ; Post . for Postulate ; and S. for Scholium . In referring to the same Book , the number of the Book is not given ; in referring to any other Book , the number of the Book is given . PROPOSITION I. THEOREM . If a straight line ...
... Problem ; Post . for Postulate ; and S. for Scholium . In referring to the same Book , the number of the Book is not given ; in referring to any other Book , the number of the Book is given . PROPOSITION I. THEOREM . If a straight line ...
Page 81
... and DC , The angle CAE , which is the difference of DAE and DAC , is measured by half the difference of the arcs DCA and DC , or by half the arc CA. PRACTICAL APPLICATIONS . PROBLEM I. To bisect a given straight BOOK III . 81.
... and DC , The angle CAE , which is the difference of DAE and DAC , is measured by half the difference of the arcs DCA and DC , or by half the arc CA. PRACTICAL APPLICATIONS . PROBLEM I. To bisect a given straight BOOK III . 81.
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence