## 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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**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 given angle , DE perpendic- ular to AB , and FG perpendicular to AC . P D B Then we shall have ... Page 20

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**perpen**- dicular can be drawn to this line . A D C B If there could be two perpendiculars , as CD and CE , the angles BCD and BCE would be equal , each being a right angle ; that is , the whole would be equal to its part , which is im ... Page 22

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**perpen**- dicular through C , its middle point . A D E F G B C First . Let D be any point in this**perpen**- dicular . Drawing DA and DB , we know these lines to be equal , since they terminate at equal distances from C , the foot of the ... Page 23

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**perpen**- dicular to the second line and bisect it . THEOREM XIV . If a line be drawn bisecting a given angle , that is , dividing it into two equal angles : I. Any point in this bisecting line will be equidistant from the sides of the ... Page 39

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**perpen**- dicularly to BC , AC , AB , will be the same as the three**perpen**- diculars bisecting the sides of the triangle DEF , which**perpen**- diculars we already know must intersect each other in the same point ( T. XXXVII . ) . Hence ...### 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