Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
Dentro del libro
Página 27
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is ... to the angle EAF : wherefore the given rectilineal angle BAC is bisected by the straight line AF .
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is ... to the angle EAF : wherefore the given rectilineal angle BAC is bisected by the straight line AF .
Página 28
To bisect a given finite straight line , that is , to divide it into two equal parts . > Let AB be the given straight line ; it is required to divide it into two equal parts . Describe ( 1. 1. ) upon it an equilateral triangle ABC ...
To bisect a given finite straight line , that is , to divide it into two equal parts . > Let AB be the given straight line ; it is required to divide it into two equal parts . Describe ( 1. 1. ) upon it an equilateral triangle ABC ...
Página 29
the circle EGF meeting AB in F , G ; and A E H G B bisect ( 10. 1. ) FG in H , and D join CF , CH , CG ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB .
the circle EGF meeting AB in F , G ; and A E H G B bisect ( 10. 1. ) FG in H , and D join CF , CH , CG ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB .
Página 31
Bisect ( 10. 1. ) AC in E , join E BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ... BC be bisected , it may be demonstrated that the OF GEOMETRY .
Bisect ( 10. 1. ) AC in E , join E BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ... BC be bisected , it may be demonstrated that the OF GEOMETRY .
Página 32
BC be bisected , it may be demonstrated that the angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together ...
BC be bisected , it may be demonstrated that the angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Información bibliográfica
| Título | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
| Autor | John Playfair |
| Editor | E. Duyckinck, and George Long, 1824 |
| Procedencia del original | Universidad de Indiana |
| Digitalizado | 15 Ene. 2009 |
| Largo | 333 páginas |
| Exportar cita | BiBTeX EndNote RefMan |