## 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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**correspond**to analogous subjects . We have also ar- ranged the Problems by themselves , and have in no case mixed them up with the Theorems . In the preparation of the Geometrical portion of this work , we have made free use of the ... Page 15

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**corresponding**sides parallel are either equal or supplementary . First . When the sides AB and AC , forming the angle at A , have respectively the same directions as the sides DE and DF forming the angle at D. F B K D E G H Produce CA ... Page 16

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**corresponding**side . F FH C B K G A B E K D G H As before , the angle BAC is equal to KGC , and EDF is equal to EGC . But KGC and EGC are supplementary ( T. I. ) , consequently BAC and EDF are supplementary . Cor . Two angles having ... Page 17

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**corresponding**in- terior angles are denoted by the small let- ters a , b , c , etc. Now any exterior angle , together with its ad- jacent interior angle , as A + a , is equal to two right angles ( T. I. ) , therefore the sum of all the ... Page 26

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**corresponding**angles are equal . First . Suppose EGB + FHD = 2 right angles . We have EGB = AGH , and FHD = CHG ( T. I. ) , hence AGH + CHG = 2 right angles , which agrees with the Theorem itself , hence AB and CD are parallel ...### 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