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 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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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 |
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