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 15
than the angle ACB ; but it is not ; therefore the side AC is not less than AB ; and it B A has been shewn that it is not equal to AB ; therefore AC is greater than AB . PROP . XIII . THEOR . Any two sides of a triangle are together ...
than the angle ACB ; but it is not ; therefore the side AC is not less than AB ; and it B A has been shewn that it is not equal to AB ; therefore AC is greater than AB . PROP . XIII . THEOR . Any two sides of a triangle are together ...
Página 16
... of the triangle CED are greater than CD . if DB be added to each , the sides CE , EB , will be greater than CD , DB ; but it has been shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC .
... of the triangle CED are greater than CD . if DB be added to each , the sides CE , EB , will be greater than CD , DB ; but it has been shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC .
Página 17
... BAC is not equal to the angle EDF ; neither is it less ; because then the base BC would be less ( 15. 1. ) than the base EF ; but it is not ; therefore the angle BAC is not less than the angle D AA B EDF and it was shewn that it is ...
... BAC is not equal to the angle EDF ; neither is it less ; because then the base BC would be less ( 15. 1. ) than the base EF ; but it is not ; therefore the angle BAC is not less than the angle D AA B EDF and it was shewn that it is ...
Página 22
to the angle GKD ; and it was shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is pa- rallel ( 19. 1. ) to CD . F A G B E H K с D PROP . XXIV .
to the angle GKD ; and it was shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is pa- rallel ( 19. 1. ) to CD . F A G B E H K с D PROP . XXIV .
Página 23
Again , because AB is parallel to CE , and BD falls upon them , the exterior an- gle ECD is equal to the interior and opposite angle ABC , but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole ex- terior angle ...
Again , because AB is parallel to CE , and BD falls upon them , the exterior an- gle ECD is equal to the interior and opposite angle ABC , but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole ex- terior angle ...
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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 |