Elements of Geometry and Trigonometry |
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Page 29
... less than BC ; or , since GC EF , we have , D A = BC > EF . B G CE 3 ° . When G is within the triangle ABC . From ... less than , would be equal to EF ( P. V. ) , and in the latter case , BC would be less than EF ; either of which would ...
... less than BC ; or , since GC EF , we have , D A = BC > EF . B G CE 3 ° . When G is within the triangle ABC . From ... less than , would be equal to EF ( P. V. ) , and in the latter case , BC would be less than EF ; either of which would ...
Page 30
... less than D , the side BC would be less than EF . But BC is equal to EF , by hypothesis ; therefore , the angle A can neither be greater nor less than D : hence , it must be equal to it . The two triangles have , therefore , two sides ...
... less than D , the side BC would be less than EF . But BC is equal to EF , by hypothesis ; therefore , the angle A can neither be greater nor less than D : hence , it must be equal to it . The two triangles have , therefore , two sides ...
Page 32
... less than ABC , the side AB would be less than the side AC , from what has just been proved ; if ACB were equal to ABC , the side AB would be equal to AC , by Prop . XII .; but both conditions are contrary to the hypothesis : hence ...
... less than ABC , the side AB would be less than the side AC , from what has just been proved ; if ACB were equal to ABC , the side AB would be equal to AC , by Prop . XII .; but both conditions are contrary to the hypothesis : hence ...
Page 33
... less than , nor equal to , ABC ; it must , therefore , be greater ; which was to be proved . PROPOSITION XIV . THEOREM . From a given point only one perpendicular can be drawn to a given straight line . Let A be a given point , and AB ...
... less than , nor equal to , ABC ; it must , therefore , be greater ; which was to be proved . PROPOSITION XIV . THEOREM . From a given point only one perpendicular can be drawn to a given straight line . Let A be a given point , and AB ...
Page 34
... less than any of the oblique lines , AC will be equal to AE , and AD greater than AC . A D B E F Prolong AB until BF is equal to AB , and draw FC , FD . 1o . In the triangles ABC , FBC , we have the side AB equal to BF , by construction ...
... less than any of the oblique lines , AC will be equal to AE , and AD greater than AC . A D B E F Prolong AB until BF is equal to AB , and draw FC , FD . 1o . In the triangles ABC , FBC , we have the side AB equal to BF , by construction ...
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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...