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 |
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Página 30
Again , the angle DBA is equal to the two angles DBE , EBA ; add to each of these equals the apgle ABC ; then will the two angles DBA , ABC be equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been demonstrated ...
Again , the angle DBA is equal to the two angles DBE , EBA ; add to each of these equals the apgle ABC ; then will the two angles DBA , ABC be equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been demonstrated ...
Página 31
In the same manner it may be demonstrated that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that if two straight lines cut one anotber , the angles which they ...
In the same manner it may be demonstrated that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that if two straight lines cut one anotber , the angles which they ...
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 ...
Página 33
Io the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. PROP . XXI . THEOR . > If from the OF GEOMETRY . BOOK I. 33.
Io the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. PROP . XXI . THEOR . > If from the OF GEOMETRY . BOOK I. 33.
Página 34
... for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC .
... for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC .
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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 |