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 Restored : Also the Book of Euclid's Data, in Like Manner CorrectedJ. Nourse, London, 1781 - 520 sider |
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Resultat 1-5 av 96
Side 48
... fquare upon AB . E From the point A draw a AC at right angles to AB ; and make AD equal to AB , and through the point D draw DE parallel to AB , and through B draw BE parallel to AD ; there- fore ADEB is a parallelogram ; whence AB is ...
... fquare upon AB . E From the point A draw a AC at right angles to AB ; and make AD equal to AB , and through the point D draw DE parallel to AB , and through B draw BE parallel to AD ; there- fore ADEB is a parallelogram ; whence AB is ...
Side 49
... fquare GB : And in the fame manner , by joining AE , BK , it is demonstrated that the parallelogram CL is equal to the fquare HC : Therefore the whole square BDEC is equal to the two fquares GB , HC ; and the fquare BDEC is described ...
... fquare GB : And in the fame manner , by joining AE , BK , it is demonstrated that the parallelogram CL is equal to the fquare HC : Therefore the whole square BDEC is equal to the two fquares GB , HC ; and the fquare BDEC is described ...
Side 50
... fquare described upon BC , one of the fides of the tri- angle ABC , be equal to the fquares upon the other fides BA ... fquare of DA is equal to the fquare of AB : To each of these add the fquare of AC ; therefore the squares of DA , AC ...
... fquare described upon BC , one of the fides of the tri- angle ABC , be equal to the fquares upon the other fides BA ... fquare of DA is equal to the fquare of AB : To each of these add the fquare of AC ; therefore the squares of DA , AC ...
Side 52
... fquare ADEB , and through C draw b CF , parallel to AD , or BE ; then AE is equal to the rectangles AF , CE ; and AE is the fquare of AB ; D F E and N. B. To avoid repeating the word contained too frequently , the rectangl contained by ...
... fquare ADEB , and through C draw b CF , parallel to AD , or BE ; then AE is equal to the rectangles AF , CE ; and AE is the fquare of AB ; D F E and N. B. To avoid repeating the word contained too frequently , the rectangl contained by ...
Side 53
... fquare of the forefaid part . Let the ftraight line AB be divided into any two parts in the point C ; the rectangle AB , BC is equal to the rectangle AC , CB , together with the fquare of BC . Upon BC defcribe the fquare A CDEB , and ...
... fquare of the forefaid part . Let the ftraight line AB be divided into any two parts in the point C ; the rectangle AB , BC is equal to the rectangle AC , CB , together with the fquare of BC . Upon BC defcribe the fquare A CDEB , and ...
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The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fides BA fimilar fince firft firſt folid angle fome fore fphere 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 oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC vertex wherefore