Elements of Geometry and Trigonometry |
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Page 14
... common point A , is called the ver- C A B tex . An angle is designated by naming its sides , or some- times by simply naming its vertex ; thus , the above is called the angle BAC , or simply , the angle A. 11. When one straight line ...
... common point A , is called the ver- C A B tex . An angle is designated by naming its sides , or some- times by simply naming its vertex ; thus , the above is called the angle BAC , or simply , the angle A. 11. When one straight line ...
Page 22
... common A angle ACE ( A. 3 ) , there re- mains , ACD = ECB . D E B In like manner , we find , ACD + ACE = ACD + DCB ; and , taking away the common angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the ...
... common A angle ACE ( A. 3 ) , there re- mains , ACD = ECB . D E B In like manner , we find , ACD + ACE = ACD + DCB ; and , taking away the common angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the ...
Page 23
... common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will A the lines coincide throughout . Between A and B they must E B C D coincide ( A. 11 ) ...
... common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will A the lines coincide throughout . Between A and B they must E B C D coincide ( A. 11 ) ...
Page 24
... common angle DCA , there re- mains , DCB = DCE , which is impossible , since a part cannot be equal to the whole ( A. 8 ) . Hence , CB must be the prolongation of AC ; which was to be proved . PROPOSITION V. THEOREM . If two triangles ...
... common angle DCA , there re- mains , DCB = DCE , which is impossible , since a part cannot be equal to the whole ( A. 8 ) . Hence , CB must be the prolongation of AC ; which was to be proved . PROPOSITION V. THEOREM . If two triangles ...
Page 29
... common part AB , there remains ( A. 5 ) , BC > EF 2o . When G is on BC . In this case , it is obvious that GC is 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 ...
... common part AB , there remains ( A. 5 ) , BC > EF 2o . When G is on BC . In this case , it is obvious that GC is 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 ...
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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...