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, Edlemnts of Plane and Spherical Trigonometry |
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Página 14
to two right angles : there- fore the angles ABC , BCA are less than two right angles . In like man- ner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . B PROP . XI . THEOR .
to two right angles : there- fore the angles ABC , BCA are less than two right angles . In like man- ner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . B PROP . XI . THEOR .
Página 24
to two right angles ; there- fore all the interior , together with all the exterior angles of the figure , are equal to twice as many right angles as there are sides of the figure ; that is , they are equal to all the interior angles of ...
to two right angles ; there- fore all the interior , together with all the exterior angles of the figure , are equal to twice as many right angles as there are sides of the figure ; that is , they are equal to all the interior angles of ...
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Produce AD both ways to the points E , F , and through B draw BE parallel to CA ; and through C draw CF parallel to BD : There- fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equal ( 29. 1. ) ...
Produce AD both ways to the points E , F , and through B draw BE parallel to CA ; and through C draw CF parallel to BD : There- fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equal ( 29. 1. ) ...
Página 31
There- fore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is described upon the straight line BC , and the squares GB , HC upon BA , AC : wherefore the square upon the side BC is equal to the squares ...
There- fore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is described upon the straight line BC , and the squares GB , HC upon BA , AC : wherefore the square upon the side BC is equal to the squares ...
Página 32
to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; there- fore CA , CB are each of them equal to AB ; now things which are equal to the ...
to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; there- fore CA , CB are each of them equal to AB ; now things which are equal to the ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Vista de fragmentos - 1836 |
Términos y frases comunes
ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid spherical square straight line taken tangent THEOR third touch 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, Edlemnts of Plane and Spherical Trigonometry |
| Autor | John Playfair |
| Edición | 6 |
| Editor | W.E. Dean, 1836 |
| Largo | 311 páginas |
| Exportar cita | BiBTeX EndNote RefMan |