## Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |

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ABCD altitude axis base called centre chord circle circumference circumscribed coincide common cone consequently construct corresponding cosine cotangent cylinder denote described diameter difference distance divided draw drawn edges equal Equation EXAMPLES extremity faces feet figure formed Formula four frustum functions given greater half hence homologous included inscribed intersection lateral less logarithm manner mean measured meet multiplied opposite parallel parallelogram parallelopipedon pass perimeter perpendicular placed plane plane MN polyedron polygon positive prism PROBLEM proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular right angles RULE Scholium segment shown sides similar sine solution sphere spherical triangle square straight line taken tangent term THEOREM third triangle triangle ABC unit upper vertex vertices volume whence

### Popular passages

Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.

Page 69 - 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 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.

Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.

Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 28 - If two triangles have two sides of the one equal to two sides of the...

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

Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.

Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.