# Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States

A.S. Barnes, 1885 - Geometry - 512 pages
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### Contents

 Exercises 163 Exercises 187 Exercises 221 Cylinder Cone and Sphere 223 Exercises 248 Exercises 277 PLANE TRIGONOMETRY 3 Multiplication by Logarithms 11 11 PLANE TRIGONOMETRY 17
 Quadrantal Triangles 89 89 Solution of Obliqueangled Triangles 98116 98 MENSURATION 117 Area of a Trapezoid 125 125 Area of a Circle 131 131 Area of the Surface of a Prism 134 136 Volume of a Prismoid 144 144 Logarithms of Numbers from 1 to 10000 116 1 Sines and Tangents 1762 17

### Popular passages

Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - 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 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.