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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 34
... angle BAC . Produce BD to E ; and because two sides of a triangle ( 20. 1. ) are greater than the third side , the two sides BA , AE of the triangle ABE are greater than BE . To each of these add EC ; therefore the sides BA , AC are ...
... angle BAC . Produce BD to E ; and because two sides of a triangle ( 20. 1. ) are greater than the third side , the two sides BA , AE of the triangle ABE are greater than BE . To each of these add EC ; therefore the sides BA , AC are ...
Página 36
... angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . PROP . XXIV . THEOR . If two ... BAC greater than the angle EDF ; the base BC is also greater than the base EF . Of the two sides DE , DF , let DE be the ...
... angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . PROP . XXIV . THEOR . If two ... BAC greater than the angle EDF ; the base BC is also greater than the base EF . Of the two sides DE , DF , let DE be the ...
Página 37
... angle BAC is likewise greater than the angle EDF . For , if it be not greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base BC would be equal ( 4. 1. ) to EF ; but it ...
... angle BAC is likewise greater than the angle EDF . For , if it be not greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base BC would be equal ( 4. 1. ) to EF ; but it ...
Página 38
... angle ABC is equal to the angle DEF , therefore the base AC is equal ( 4. 1. ) to the base DF , and the angle BAC to the angle EDF . Next , let the sides which are opposite to equal angles in each tri- angle be equal to one an- other ...
... angle ABC is equal to the angle DEF , therefore the base AC is equal ( 4. 1. ) to the base DF , and the angle BAC to the angle EDF . Next , let the sides which are opposite to equal angles in each tri- angle be equal to one an- other ...
Página 41
... angle GHF . A- gain , because the straight line GK cuts the parallel ... angles ; therefore AB is parallel ( 27.1 . ) to CD . Where- fore straight lines , & c ... BAC , ACE are equal ( 29 . 1. ) Again , because AB is B A E C D F parallel ...
... angle GHF . A- gain , because the straight line GK cuts the parallel ... angles ; therefore AB is parallel ( 27.1 . ) to CD . Where- fore straight lines , & c ... BAC , ACE are equal ( 29 . 1. ) Again , because AB is B A E C D F parallel ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore