The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner CorrE. Wingrove, London, and J. Balfour, Edinburgh, 1793 - 520 páginas |
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Página 49
... AC , AG upon the oppofite fides of AB , make with it at the point A the adjacent angles equal to two right angles ... square BDEC is equal to the two fquares GB , HC ; and the fquare BDEC is described upon the straight line BC , and the ...
... AC , AG upon the oppofite fides of AB , make with it at the point A the adjacent angles equal to two right angles ... square BDEC is equal to the two fquares GB , HC ; and the fquare BDEC is described upon the straight line BC , and the ...
Página 53
... AC ; for it is contained by DA , AC , of which AD is equal to AB ; and CE is contained by AB , BC , for BE is equal ... square of BC ; therefore the rectangle AB , D Book II . یم Ba 46. I. b 31. I. BC is equal to the rectangle AC , CB ...
... AC ; for it is contained by DA , AC , of which AD is equal to AB ; and CE is contained by AB , BC , for BE is equal ... square of BC ; therefore the rectangle AB , D Book II . یم Ba 46. I. b 31. I. BC is equal to the rectangle AC , CB ...
Página 54
... square , and it is upon the fide HG , which is equal to AC : Therefore HF , CK are the squares of AC , CB ; and because the complement AG is equal g to the complement GE , and that AG is the rectangle contain- ed by AC , CB , for GC is ...
... square , and it is upon the fide HG , which is equal to AC : Therefore HF , CK are the squares of AC , CB ; and because the complement AG is equal g to the complement GE , and that AG is the rectangle contain- ed by AC , CB , for GC is ...
Página 55
... square of CD , is equal to the fquare of CB . Upon CB defcribe a the fquare ... AC is equal to K A C D B L H d 36. I M CB ; therefore alfo AL is equal to DF ... square of CB . Wherefore , if a ftraight line , & c . Q. E. D. From this ...
... square of CD , is equal to the fquare of CB . Upon CB defcribe a the fquare ... AC is equal to K A C D B L H d 36. I M CB ; therefore alfo AL is equal to DF ... square of CB . Wherefore , if a ftraight line , & c . Q. E. D. From this ...
Página 59
... AC or CB , and join EA , EB ; through D draw E G F CD B b DF parallel to CE , and through F draw FG parallel to AB ; b 31. 1 , and join AF : Then , because AC ... square of GF ; therefore the fquares of FG , GF are double of the g 47. I. b 34 ...
... AC or CB , and join EA , EB ; through D draw E G F CD B b DF parallel to CE , and through F draw FG parallel to AB ; b 31. 1 , and join AF : Then , because AC ... square of GF ; therefore the fquares of FG , GF are double of the g 47. I. b 34 ...
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Términos y frases comunes
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fecond fegment fhall fide BC fides fimilar firft firſt folid angle fome fore fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepiped parallelogram perpendicular plane angles PROP propofition proportionals pyramid rectangle contained rectilineal figure right angles ſame ſhall ſphere ſquare THEOR theſe tiple triangle ABC wherefore