## 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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**divided**by producing either of the sides CD or FD . This polygon is said to have a re - entering angle at D. G C Ꭰ A B THEOREM V. In any convex polygon , the sum of all the interior angles , taken together , is equal to twice as many ... Page 48

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**divided**into equal portions , each of which shall be less than arc GH , there will be at least one point of division between G and II , as at K. Draw the ra- dius EK , and then since the arcs AB and AK are commensura- ble , we have by ... Page 75

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**divided**into 7 + 11 = 18 equal parts , and through the points of division parallels to BC to be drawn , they will divide DC into 18 equal parts ( T. I. ) , of which 7 will belong to DF , and 11 to FC . Hence , DF : FC :: 7 : 11 ... Page 83

... CD ' , just demonstrated , we deduce the following : BD : CD :: BD ' : CD ' ; and the straight line BC is said to be

... CD ' , just demonstrated , we deduce the following : BD : CD :: BD ' : CD ' ; and the straight line BC is said to be

**divided**harmonically at the points D and D ' . THEOREM XIII . If from the right angle of a THIRD BOOK . 83. Page 94

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**divided**by twice the diameter of its circumscribed circle . Let K be the centre of the circumscribed circle . Draw the diameter CKD , and the chord AD , and the perpendicular CH , which will be the altitude of the triangle . D K B H The ...### 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