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 sider |
Inni boken
Resultat 1-5 av 56
Side 49
... square BDEC is equal to the two fquares GB , HC ; and the fquare BDEC is described upon the straight line BC , and the fquares GB , HC upon BA , AC : Wherefore the fquare upon the fide BC is e- qual to the fquares upon the fides BA , AC ...
... square BDEC is equal to the two fquares GB , HC ; and the fquare BDEC is described upon the straight line BC , and the fquares GB , HC upon BA , AC : Wherefore the fquare upon the fide BC is e- qual to the fquares upon the fides BA , AC ...
Side 53
... 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 together with the square of BC . If therefore a straight , & c . Q. E. D. IF PROP . IV . THEOR . F a ftraight line be ...
... 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 together with the square of BC . If therefore a straight , & c . Q. E. D. IF PROP . IV . THEOR . F a ftraight line be ...
Side 54
... square of AB : Therefore the square of AB is equal to the fquares of AC , CB and twice the rectangle AC , CB . Wherefore if a straight line , & c . Q. E. D. COR . From the demonftration , it is manifest that the pa rallelograms about ...
... square of AB : Therefore the square of AB is equal to the fquares of AC , CB and twice the rectangle AC , CB . Wherefore if a straight line , & c . Q. E. D. COR . From the demonftration , it is manifest that the pa rallelograms about ...
Side 55
... square of CD , is equal to the fquare of CB . Upon CB defcribe a the fquare CEFB , join BE , and through a 46. I. D draw b DHG parallel to CE or BF ; and through H draw b 31. 1 . KLM parallel to CB or EF ; and alfo through A draw AK pa ...
... square of CD , is equal to the fquare of CB . Upon CB defcribe a the fquare CEFB , join BE , and through a 46. I. D draw b DHG parallel to CE or BF ; and through H draw b 31. 1 . KLM parallel to CB or EF ; and alfo through A draw AK pa ...
Side 59
... fquare of EA is double of the fquare of AC : Again , be- caufe EG is equal to GF , the fquare of EG is equal to the square of GF ; therefore the fquares of FG , GF are double of the g 47. I. b 34. I. i 47. I. Book II . the OF EUCLID . 59.
... fquare of EA is double of the fquare of AC : Again , be- caufe EG is equal to GF , the fquare of EG is equal to the square of GF ; therefore the fquares of FG , GF are double of the g 47. I. b 34. I. i 47. I. Book II . the OF EUCLID . 59.
Andre utgaver - Vis alle
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1781 |
Vanlige uttrykk og setninger
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