Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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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 , they will have a common altitude : hence , ( P. VI . , CE A D 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 ...
... vertices at the same point E , they will have a common altitude : hence , ( P. VI . , CE A D 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 ...
Page 133
... vertices B and G lie in the B E F D 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 B E F D 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
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence