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

### From inside the book

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**Ratios**between the areas of similar figures Comparison of squares constructed on certain lines FOURTH BOOK ...**Ratio**of the circumference to its diameter .... 121 PROBLEMS . Construction of proportional lines . 126 Problems of ... Page 12

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**ratio**can be accurately expressed : but many magnitudes are incommensurable ; that is , their**ratio**can be expressed only by approximation ; which approximation may , however , be carried to any extent we desire . Such is the**ratio**of ... Page 70

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**ratio**. Let AB and CD be the given lines . From the greater AB cut off parts equal to the less line CD , as many times as possible ; for example , twice , with the remainder FB . From the line CD cut off parts equal to FB , as many ... Page 71

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**ratio**shall approximate as close as we please to the**ratio**of the given incommensurable magnitudes . This being admitted , we say that two incommensurable mag- nitudes A and B are proportional to two other incommensurable magnitudes ... Page 73

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**ratio**of these lines , which is always the same , is called the**ratio**of similitude . When the**ratio**of similitude is equal to unity , the two similar figures become equal in all respects . II . Two triangles are similar when their ...### 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