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 22
... angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the angles about C all of the ... ACB , BCD , DCE , ECF , FCA , that can be formed about a point , is equal to four right angles . F B 租-D For , if ...
... angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the angles about C all of the ... ACB , BCD , DCE , ECF , FCA , that can be formed about a point , is equal to four right angles . F B 租-D For , if ...
Page 31
... angle B is equal to the angle C ; which was to be proved . B4 D Cor . 1. An ... ACB : then will AC be equal to AB , and consequently , the triangle will be ... angle ACB equal to the included angle DBC , by hypothesis : hence , the two ...
... angle B is equal to the angle C ; which was to be proved . B4 D Cor . 1. An ... ACB : then will AC be equal to AB , and consequently , the triangle will be ... angle ACB equal to the included angle DBC , by hypothesis : hence , the two ...
Page 32
... angle is opposite the greater side . In the triangle ABC , let the angle ACB be greater than the angle ABC : then will the side AB be greater than the side AC . For , draw CD , making the angle BCD equal to the angle B ( Post . 7 ) ...
... angle is opposite the greater side . In the triangle ABC , let the angle ACB be greater than the angle ABC : then will the side AB be greater than the side AC . For , draw CD , making the angle BCD equal to the angle B ( Post . 7 ) ...
Page 33
... angles ABC and FBC equal , because both are right an- gles hence , the angles ACB and FCB are equal ( P. V. ) But ACB is , by a hypothesis , a right angle : hence , FCB must also be a right angle , and consequently , the line ACF must ...
... angles ABC and FBC equal , because both are right an- gles hence , the angles ACB and FCB are equal ( P. V. ) But ACB is , by a hypothesis , a right angle : hence , FCB must also be a right angle , and consequently , the line ACF must ...
Page 74
... angles ACB and DOE be commensurable ; that is , be exactly measured by a common unit : then will they be proportional to the intercepted arcs AB and DE . M and suppose , for Let the angle M be a common unit ; example , that this unit is ...
... angles ACB and DOE be commensurable ; that is , be exactly measured by a common unit : then will they be proportional to the intercepted arcs AB and DE . M and suppose , for Let the angle M be a common unit ; example , that this unit is ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin 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 polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence