## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |

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Page 121

... , will become 16 A ' = √8 , B ' = 2 + √8 = 4 ( √8 − 2 ) , which , converted into

... , will become 16 A ' = √8 , B ' = 2 + √8 = 4 ( √8 − 2 ) , which , converted into

**decimals**, will give 2.8284271 , etc. , 3.3137085 , etc. , for the areas , respectively , FOURTH BOOK . 121 Ratio of the circumference to its diameter. Page 122

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**decimals**. No. of sides . Area of the inscribed polygon . 2.0000000 Area of the circumscribed polygon . 4 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 256 ... Page 124

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**decimals**, in the following table : No. of sides . Apothems . Radii . 4 0.5000000 0.7071068 8 0.6035534 0.6532815 16 ...**decimal**places . The value to thirty - one**decimals**is T = 3.1415926535897932384626433832795 . The following ... Page 125

... . , - which is the ratio true to six

... . , - which is the ratio true to six

**decimals**. For simplicity and ac- curacy , a better graphic method of finding this ratio can hardly be expected , or even desired . PROBLEMS , WHICH REFER TO THE THIRD AND FOURTH BOOKS FOURTH BOOK . 125. Page 12

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**decimal**figure , we may find the cosine of 1 ' as follows ( § 8 ) : cos . 1 ' = √1 - sin . 1 ' = 0.9999999577 , & c . Having thus found the sine and cosine of 1 ' , we may continue our work for larger angles by the aid of equations ( 1 ) ...### Other editions - View all

### Common terms and phrases

a+b+c ACē altitude angles equal apothem bisect centre chord circ circumference cone consequently corresponding cosec Cosine Cotang cylinder decimal denote described diameter dicular distance divided draw drawn equation equivalent exterior angles feet figure formed frustum give given line greater half hence homologous sides hypotenuse inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle Scholium secant sector similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism vertex volume