Elements of Geometry and Trigonometry |
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Page 7
... a Circle , 116 To find the Diameter of a Circle , 116 To find the length of an Arc , 117 Area of a Circle , Area of a Sector , Area of a Segment , Area of a Circular Ring , 117 118 118 119 PAGE . Area of the Surface of a Prism , CONTENTS .
... a Circle , 116 To find the Diameter of a Circle , 116 To find the length of an Arc , 117 Area of a Circle , Area of a Sector , Area of a Segment , Area of a Circular Ring , 117 118 118 119 PAGE . Area of the Surface of a Prism , CONTENTS .
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 3.3137,085 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 3.3137,085 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 radins by R , and the area of a circle whose radius is 1 , by « × 1 ' ( 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 radins by R , and the area of a circle whose radius is 1 , by « × 1 ' ( P. XII ...
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Common terms and phrases
ABCD AC² adjacent angles altitude angle ACB 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 distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence