Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 60
... vertices are in the circumfer- ence , and whose sides are chords . 10. A SECANT is a straight line which · cuts the circumference in two points . 11. A TANGENT is a straight line which touches the circumference in one point . This point ...
... vertices are in the circumfer- ence , and whose sides are chords . 10. A SECANT is a straight line which · cuts the circumference in two points . 11. A TANGENT is a straight line which touches the circumference in one point . This point ...
Page 89
... vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle . There may be two cases : the given point may lie on the circumference of the given circle ...
... vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle . There may be two cases : the given point may lie on the circumference of the given circle ...
Page 110
... vertices at the same point E , have a common altitude : hence , ( P. VI . , CE . E C. ) AED : DEB :: AD : DB . B The triangles AED and EDC , have their bases in the same line AC , and their vertices at the same point D ; they have ...
... vertices at the same point E , have a common altitude : hence , ( P. VI . , CE . E C. ) AED : DEB :: AD : DB . B The triangles AED and EDC , have their bases in the same line AC , and their vertices at the same point D ; they have ...
Page 133
... vertices B and G lie in the A E F same line BG parallel to the base , their altitudes are equal , and consequently , the triangles are equal : hence , the polygon GCDE is equal to the polygon ABCDE . Again , draw CE ; produce AE and ...
... vertices B and G lie in the A E F same line BG parallel to the base , their altitudes are equal , and consequently , the triangles are equal : hence , the polygon GCDE is equal to the polygon ABCDE . Again , draw CE ; produce AE and ...
Page 137
... vertices : hence , it is circumscribed about the polygon ; which was to be proved . 2o . A circle may be inscribed in the polygon . For , the sides AB , BC , & c . , being equal chords of the circumscribed circle , are equidistant from ...
... vertices : hence , it is circumscribed about the polygon ; which was to be proved . 2o . A circle may be inscribed in the polygon . For , the sides AB , BC , & c . , being equal chords of the circumscribed circle , are equidistant from ...
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Common terms and phrases
ABē ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following