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 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 .
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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. ) ...
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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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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
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 | B. & S. Collins; W. E. Dean, printer, 1836 |
| Largo | 311 páginas |
| Exportar cita | BiBTeX EndNote RefMan |