## 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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**subtraction**, we obtain EC = DE - DC ; that is , one side of a triangle is equal to the difference of the other two sides , which is impossible ( B. I. , T. VII . ) . Hence the side DC cannot be secant . In a similar way we can show ... Page 71

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**subtracting**the angle ABF from ABG , the remainder FBG will equal the angle BFG , found by**subtracting**the angle AFB from AFG . Consequently the triangle BGF is isosceles , and BGFG ; but , since AC is the diagonal SECOND BOOK . 71. Page 88

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**subtract**the triangle BEC , we shall have left the parallelogram ABCD ; but if from the same quadrilateral we**subtract**the equal triangle AFD , we shall have left the parallelogram ABEF . Hence the two parallelograms are equivalent . We ... Page 211

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**subtracting**( 1 ) from it , we have , after a slight reduction , x + y = b2 - a2 2c 50 feet , the required height . PROBLEM III . A statue eighty feet high stands on a pedestal fifty feet high , and to a spectator on the horizontal ... Page 213

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**subtract**each side separately ; then take the square root of the continued product of the half sum and the three remain- ders , and it will be the area . PROBLEM V. Given the three sides a , b , c of a triangle , to find : 1. The three ...### 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