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 41
... circle included by an arc and its chord is called a segment . The portion included between two radii and the ... circumscribed about the circle . By an angle in a segment of a circle , is to be understood an angle whose vertex is ...
... circle included by an arc and its chord is called a segment . The portion included between two radii and the ... circumscribed about the circle . By an angle in a segment of a circle , is to be understood an angle whose vertex is ...
Page 51
... CIRCUMSCRIBED POLYGONS . THEOREM XII . All triangles are capable of being inscribed in a circle and of circumscribing a circle . First . The three perpendiculars bisecting the three sides of the triangle ABC , meet in C E F the same ...
... CIRCUMSCRIBED POLYGONS . THEOREM XII . All triangles are capable of being inscribed in a circle and of circumscribing a circle . First . The three perpendiculars bisecting the three sides of the triangle ABC , meet in C E F the same ...
Page 52
... circle . Hence , if lines be drawn bi- secting the angles , and the exterior angles of a triangle , they will ... circumscribed and inscribed circles will then be concentric . THEOREM XIII . In any inscribed quadrilateral , the sum ...
... circle . Hence , if lines be drawn bi- secting the angles , and the exterior angles of a triangle , they will ... circumscribed and inscribed circles will then be concentric . THEOREM XIII . In any inscribed quadrilateral , the sum ...
Page 55
... circle will be inscribed in the polygon , and the polygon will circumscribe the circle . 1 Scholium . The point F , the common centre of the inscribed and circumscribed circles , is called the centre of the regular polygon . The radius ...
... circle will be inscribed in the polygon , and the polygon will circumscribe the circle . 1 Scholium . The point F , the common centre of the inscribed and circumscribed circles , is called the centre of the regular polygon . The radius ...
Page 56
... circle , we draw tangents , we shall thus circumscribe a regular polygon of the same number of sides . A " E B A ' B A E " C D M D D ' מי The tangents thus drawn will form with the sides of the inscribed polygon , AB , BC , CD , etc ...
... circle , we draw tangents , we shall thus circumscribe a regular polygon of the same number of sides . A " E B A ' B A E " C D M D D ' מי The tangents thus drawn will form with the sides of the inscribed polygon , AB , BC , CD , etc ...
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Common terms and phrases
ABē ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum GEOMETRY given angle given line gives greater half hence homologous hypotenuse inches included angle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume