Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page vii
... Area of a Parallelogram , ... 106 The Area of a Triangle , 106 ..... Formula for the Sine of Half an Angle , .. 108 Area of a Trapezoid , 112 Area of a Quadrilateral , 112 Area of a Polygon , 113 Area of a Regular Polygon , 114 To find ...
... Area of a Parallelogram , ... 106 The Area of a Triangle , 106 ..... Formula for the Sine of Half an Angle , .. 108 Area of a Trapezoid , 112 Area of a Quadrilateral , 112 Area of a Polygon , 113 Area of a Regular Polygon , 114 To find ...
Page 149
... area of a regular inscribed polygon , and that of a similar circumscribed polygon being given , to find the areas of the regular inscribed and circumscribed polygons having double the number of sides . Let AB be the side of the given ...
... area of a regular inscribed polygon , and that of a similar circumscribed polygon being given , to find the areas of the regular inscribed and circumscribed polygons having double the number of sides . Let AB be the side of the given ...
Page 151
... find P ' . PROPOSITION XII . PROBLEM . To find the approximate area of a circle whose radius is 1 . The area of an inscribed square is equal to twice the square described on the radius ( P. III . , S. ) , which square is the unit of ...
... find P ' . PROPOSITION XII . PROBLEM . To find the approximate area of a circle whose radius is 1 . The area of an inscribed square is equal to twice the square described on the radius ( P. III . , S. ) , which square is the unit of ...
Page 152
... find the areas indicated below , NUMBER OF SIDES . INSCRIBED POLYGONS . CIRCUMSCRIBED POLYGONS . 4 2.0000000 • 4.0000000 8 2.8284271 3.3137085 16 3.0614674 3.1825979 32 3.1214451 3.1517249 64 3.1365485 3.1441184 128 3.1403311 3.1422236 ...
... find the areas indicated below , NUMBER OF SIDES . INSCRIBED POLYGONS . CIRCUMSCRIBED POLYGONS . 4 2.0000000 • 4.0000000 8 2.8284271 3.3137085 16 3.0614674 3.1825979 32 3.1214451 3.1517249 64 3.1365485 3.1441184 128 3.1403311 3.1422236 ...
Page 155
... find an expression for the area of any circle in terms of its radius . Let C be the centre of a circle , and CA its radius . Denote its area by area CA , its radius by R , and the area of a circle whose radius is 1 , by π × 1a ( P. XII ...
... find an expression for the area of any circle in terms of its radius . Let C be the centre of a circle , and CA its radius . Denote its area by area CA , its radius by R , and the area of a circle whose radius is 1 , by π × 1a ( P. XII ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices 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 59 - 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.