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 31
... join BE and produce it to F , and make EF equal to BE ; join al- so FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are e- qual to CE , EF , each to each ; and the angle AEB is equal ( 15 . 1. ) to the angle ...
... join BE and produce it to F , and make EF equal to BE ; join al- so FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are e- qual to CE , EF , each to each ; and the angle AEB is equal ( 15 . 1. ) to the angle ...
Página 32
... join BD ; and because ADB is the exterior angle of the triangle BDC , it is greater ( 16. 1. ) than the B A D interior and opposite angle DCB ; but ADB is equal ( 5. 1. ) to ABD because the side AB is equal to the side AD ; therefore ...
... join BD ; and because ADB is the exterior angle of the triangle BDC , it is greater ( 16. 1. ) than the B A D interior and opposite angle DCB ; but ADB is equal ( 5. 1. ) to ABD because the side AB is equal to the side AD ; therefore ...
Página 33
... join DC . Because DA is equal to AC , the angle ADC is likewise equal ( 5. 1. ) to ACD ; but the angle BCD is greater than the angle ACD ; therefore the angle BCD is greater than the angle ADC ; B D and because the angle BCD of the ...
... join DC . Because DA is equal to AC , the angle ADC is likewise equal ( 5. 1. ) to ACD ; but the angle BCD is greater than the angle ACD ; therefore the angle BCD is greater than the angle ADC ; B D and because the angle BCD of the ...
Página 35
... join KF , KG ; the tri- angle KFG has its sides equal to the three straight lines , A , B , C. D E F L A- B C Because the point F is the centre of the circle DKL , FD is equal ( 11. Def . ) to FK ; but FD is equal to the straight line A ...
... join KF , KG ; the tri- angle KFG has its sides equal to the three straight lines , A , B , C. D E F L A- B C Because the point F is the centre of the circle DKL , FD is equal ( 11. Def . ) to FK ; but FD is equal to the straight line A ...
Página 36
... join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is equal to the angle EDG , therefore the base BC is equal ( 4. 1. ) to the base EG ; and ...
... join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is equal to the angle EDG , therefore the base BC is equal ( 4. 1. ) to the base EG ; and ...
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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