## 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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**sector**. IV . When a straight line cuts the circum- ference of a circle it is called a secant . When a straight line touches the circumference in only one point it is called a tangent ; and the common point of the line and circumference ... Page 101

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**Sectors**, or Segments , are those which , in dif- ferent circles , correspond to equal angles at the centre . Thus , if the angles at A and A ' are equal , the arcs BC , B'C ' will be simi- lar , the**sectors**BAC , B'A'C ' will be ... Page 118

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**sector**is equal to half the product of its arc into its radius.` In effect , from the definition of a circu- lar**sector**, it follows that in the same circle two**sectors**are proportional to their angles , and consequently to their ... Page 119

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**sector**AOC , which has its angle AOC right , we have this proportion ,**sector**AOB :**sector**AOC :: arc AB : AC ; or , multiplying the two consequents by four , and denoting by C , S , the circumference and surface , or area of the circle ... Page 120

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**sectors**OAB , OA'B ' are respectively equivalent to the two triangles OBK , OB'K ' ( T. XV . , S. ) ; it therefore fol- lows that the circular trapezoid is equivalent to the right - angled BK + B'K ' trapezoid KBB'K ' , which has for ...### 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