## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |

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Page 76

... the product of the extremes is equal to the product of the means , we derive from the above proportion , AD : DB :: AE : EC , this

... the product of the extremes is equal to the product of the means , we derive from the above proportion , AD : DB :: AE : EC , this

**equation**, ADXEC = DBXAE . Now , in order to comprehend the sense which we 76 GEOMETRY . Page 85

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**equations**, AB2 = BC × BD , AC2 = BC × DC , we deduce the proportion , AB2 : AC2 :: BC × BD : BC × DC , or , :: BD : DC . In a similar manner , by combining the identical**equation**BC2 = BC2 , with the same two**equations**above , we have ... Page 86

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**equation**, using the al- gebraic formula , we shall have D BD2 AB2 + AD2 + 2AB × AD . Adding now , to each member of this , CD2 , and observing that BD2 + CD2 = BC2 , and also that AD2 + CD2 = AC2 , we shall obtain BC2AB2 + AC2 + 2AB ... Page 104

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**equations**, PA × PA ' = PB × PB ' , PA × PA ' = PB2 , which may be included in one single proposition , as follows : The product of the distances from the same point , either within or without a circle , to two points of its ... Page 105

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**equations**we obtain or CD × ( AE + BE ) = AC × BD + AD × BC , AB × CD = AC × BD + AD × BC . Scholium . This Theorem has many important applications . FIRST . To find the chord AB of the sum of two arcs AC , CB , when their chords are ...### Other editions - View all

### Common terms and phrases

a+b+c AC² 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