## 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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**equal**to two right angles . THEOREM II . If through the vertex of any angle , lines are drawn perpen- dicular**respectively**to its sides , they will form a new angle , either**equal**to the first , or supplementary to it . Let BAC be the ... Page 16

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**equal**to EDF . Secondly . When the sides AB and AC are**respectively**in opposite directions to DE and DF . As before , we have the angle BAC**equal**to KGC , and the angle EDF**equal**to EGH . But KGC is**equal**to its opposite angle EGH ... Page 24

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**respectively**from the line AB ( T. XII . , C. I. ) . E K G We are now to prove these lines**equal**. Through K , the middle of EG , draw KL perpendicular to CD , and it will also be perpendicular to AB . Now , suppose the portion of the ... Page 27

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**equal**acute angles , and four**equal**ob- tuse angles . These angles will be supplementary . Any two of the acute ...**respective**- ly supplementary angles . This being supposed , these lines will meet . For if they do not meet they ... Page 28

... equal to the two sides and the included angle of the other , the triangles will be identical , or equal in all ...

... equal to the two sides and the included angle of the other , the triangles will be identical , or equal in all ...

**respectively equal**to the two sides containing the right angle of the other . THEOREM XXI . If two triangles have ...### 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