## 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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**apothem**. The angles AGB , BGC , CGD , etc. , are called angles at the centre . The lines GA , GB , GC , etc. , which are the radii of the poly- gon , bisect the angles of the polygon . The apothems GH , GK , GL , etc. , which are the ... Page 56

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**apothem**FB bisects the angle A'FB ' at the centre ( T. XV . , S. ) . Hence , all the angles AOA ' , A'OB , BOB ' , B'OC , COC ' , etc. , are equal ; and their measuring arcs AI , IB , BK , KC , CL , etc. , are all equal . If then we ... Page 107

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**apothem**. For , the equal isosceles triangles OAB , OBC , OCD , etc. , give B OAB = AB × } of OG , OBCBC of OG , OCD = CD x of OG , & c . , & c . I Consequently , area ABCDEF = ( AB + BC + CD + etc. ) x 30G ; or , more concisely , A ... Page 116

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**apothem**— that is , into the radius of the circle . Hence , the area of the circle , which is the limit ( T. VIII . , S. ) of these polygons , has for its measure half the product of the circumference 116 GEOMETRY . Measure of the ... Page 122

... of which the radius is 1 , we shall seek the value of the radius corresponding to a given circumference . For this purpose , we will premise the following LEMMA . Having given the radius R and the

... of which the radius is 1 , we shall seek the value of the radius corresponding to a given circumference . For this purpose , we will premise the following LEMMA . Having given the radius R and the

**apothem**122 GEOMETRY .### 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