## 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 |

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ABCD altitude base called centre chord circle circumference circumscribed common comp cone consequently construction contained corresponding cosine Cotang cylinder described determine diagonal diameter difference distance divided draw drawn edges equal equations equivalent expressed extremity faces fall feet figure follows formed four frustum given greater half height hence hypothenuse included inscribed intersect length less logarithm magnitudes manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perimeter perpendicular plane polygon prism PROBLEM proportional PROPOSITION pyramid radii radius ratio reason rectangle regular remaining right angles right-angled triangle Scholium segment sides similar sine solidity sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex vertices whole

### Popular passages

Page 27 - If two triangles have two sides of the one equal to two sides of the...

Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.

Page 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.

Page 26 - The sum of any two sides of a triangle is greater than the third side.

Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...

Page 93 - The area of a parallelogram is equal to the product of its base and altitude.

Page 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...

Page 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.

Page 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.