Elements of Geometry and Trigonometry |
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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 . , D 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 ...
... vertices at the same point E , they will have a common altitude : hence , ( P. VI . , D 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 ...
Page 133
... vertices B and G lie in the 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 . CF G A E F Again , draw CE ; produce AE ...
... vertices B and G lie in the 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 . CF G A E F Again , draw CE ; produce AE ...
Page 137
... vertices : hence , it is circumscribed about the polygon ; which was to be proved . 2o . A circle may be inscribed within the polygon . For , the sides AB , BC , & c . , being equal chords of the circumscribed circle , are equidistant ...
... vertices : hence , it is circumscribed about the polygon ; which was to be proved . 2o . A circle may be inscribed within the polygon . For , the sides AB , BC , & c . , being equal chords of the circumscribed circle , are equidistant ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...