# 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

A.S. Barnes & Company, 1854 - 432 من الصفحات

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### المحتوى

 Introduct1on 13 Propositions 21 BOOK II 47 BOOK III 57 Problems relating to the First and Third Books 76 BOOK IV 87 Problems relating to the Fourth Book 122 BOOK V 135
 Problems 267 Table of Natural Sines 273 Solution of Triangles 281 Solution of RightAngled Triangles 287 ANALYTICAL PLANE TRIGONOMETRY 297 of Formulas 306 Homogeneity of Terms 313 SPHERICAL TRIGONOMETRY 321

 BOOK VI 156 BOOK VII 174 BOOK VIII 202 BOOK IX 227 PAGE 245 PLANE TRIGONOMETRY 255 Multiplication by Logarithms 261
 Napiers Analogies 329 Of Quadrantal Triangles 335 Area or Contents of a Surface 347 Area of a Regular Polygon 353 Mensuration of Solids divided into Two Parts 358 Convex Surface of a Cone 364

### مقاطع مشهورة

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