## 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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Page 39

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**vertices**draw lines parallel to the oppo- site sides , thus forming a second triangle DEF . E D B F Then will the figures ABCE , ABFC , and ADBC be parallelograms , and we have AE and AD each equal to BC ; hence , A is the middle point ... Page 41

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**vertex**is in the arc , and whose sides intercept the chord of said arc ; and by an angle at the centre , is meant one whose**vertex**is at the centre . In both cases the angles are said to be subtended by the chords or arcs which their ... Page 67

... First construction . Through the

... First construction . Through the

**vertices**A , B , C , etc. , of the inscribed polygon , draw tangents to the circumference , and they will form the polygon required Second construction . Through the ex- tremities I , K SECOND BOOK . 67. Page 68

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**vertices**of the circumscribed polygon , meet the circumference . The polygon ABCDE is regular , since the angles at the cen- tre A " OB " , B " OC " , etc. , being equal , their arcs which measure them are equal , and consequently the ... Page 107

... figures . Consequently , the isosceles triangles which have their

... figures . Consequently , the isosceles triangles which have their

**vertices**at the centre , and for bases the sides of the polygons , are each to each FOURTH BOOK . 107 Determination of the sides and of the areas of regular polygons.### 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