## 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

Results 6-10 of 27

Page 89

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**rectangles**, which will be equal , since they have equal bases and the same altitude ( T. XVIII . ) . Now , as the**rectangle**ABCD contains seven of these equal**rectangles**, while AFGD contains only four , it follows , that but therefore ... Page 90

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**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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**rectangle**is estimated in a similar manner , by measuring its sides by the same linear unit ; we shall thus obtain a second product , and the ratio of these two products is the same as that of the two**rectangles**, in ac- cordance with ... Page 92

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**rectangle**ABFG , which has the same base AB , and same altitude BF ( T. XVIII . , C. ) . But the**rectangle**ABFG is measured by AB × BF , consequently the parallelogram is measured by AB × BF . A B Cor . Parallelograms of the same base ... Page 94

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**rectangles**of the sides containing the equal angle . Referring to either figure , let the two triangles ABC , ADE have the angle at A common ; then we shall have D B A E C D C B ABC : ADE :: AB × AC : AD × AE . For , joining D and C ...### 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