## 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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**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 the ... Page 20

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**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- possible ... Page 22

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**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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**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 angle . II ... Page 46

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**dicular**; that is , EF will .equal EG , and the chords will be equally distant from the centre . B F A H C N M E 3 D K Secondly . Suppose the arc AB less than CD . Applying the portion of the figure on the left of HK upon the portion on ...### 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