## 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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**multiply**a surface by a line , a surface by a surface , and even a volume by a volume , etc. But in all these cases it ...**multiplied**. SIMILAR TRIANGLES . THEOREM IV . A straight line drawn parallel to either side of a triangle ... Page 90

... XXI . Any two rectangles are to each other as the product of their bases

... XXI . Any two rectangles are to each other as the product of their bases

**multiplied**by their altitudes . Let ABCD , AFGH be two rectangles , then will ABCD : AFGH :: AB × AD : AH × AF . F K D C G H B A Having placed 90 GEOMETRY . Page 91

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**Multiplying**the corresponding terms of these proportions together , and observing to omit AFKD , since it will occur in an antecedent and consequent , we shall have ABCD : AFGH :: AB - AD : AH - AF . Scholium . Hence we are at liberty ... Page 92

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**multiplied**by itself . The squares of the numbers 1 , 2 , 3 , etc. , are 1 , 4 , 9 , etc. From which we see that the square formed on a line of double length is quadruple ; on a line of triple length it is nine times as great , and so ... Page 95

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**Multiplying**together the corresponding terms of these pro- portions , and omitting the common term ADC which enters into the antecedent and consequent of the first couplet , we have ABC : ADE :: AB x AC : AD x AE . Cor . Whenever the ...### Other editions - View all

### Common terms and phrases

a+b+c AC² 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