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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Side 51
... rectangle contained by the two ftraight lines , is equal to the rectangles contain- ed by the undivided line , and the feveral parts of the ¡ divided line . D 2 Let i Book II . a II . I ' b 3. OF EUCLID . ST.
... rectangle contained by the two ftraight lines , is equal to the rectangles contain- ed by the undivided line , and the feveral parts of the ¡ divided line . D 2 Let i Book II . a II . I ' b 3. OF EUCLID . ST.
Side 52
... rectangle contained by A , BD , together with that contain- ed by A , DE , and that contained by A , EC . с B DEC ... rectangle BH is equal to the rectangles BK , DL , EH ; and BH is contained by A , BC , for it is contained by GB , BC ...
... rectangle contained by A , BD , together with that contain- ed by A , DE , and that contained by A , EC . с B DEC ... rectangle BH is equal to the rectangles BK , DL , EH ; and BH is contained by A , BC , for it is contained by GB , BC ...
Side 53
... rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the fquare of AB . If therefore a straight line , & c . Q. E. D. Fa IF PROP . III . THEOR . a ftraight line be divided into any two parts , the rectangle ...
... rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the fquare of AB . If therefore a straight line , & c . Q. E. D. Fa IF PROP . III . THEOR . a ftraight line be divided into any two parts , the rectangle ...
Side 54
... rectangle contain- ed by AC , CB , for GC is equal to CB ; therefore GE is alfo equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : And HF , CK are the fquares of AC , CB ; wherefore the four ...
... rectangle contain- ed by AC , CB , for GC is equal to CB ; therefore GE is alfo equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : And HF , CK are the fquares of AC , CB ; wherefore the four ...
Side 55
... rectangle con- tained by the unequal parts , together with the fquare of the line between the points of fection , is equal to the fquare of half the line . Let the straight line AB be divided into two equal parts in the point C , and ...
... rectangle con- tained by the unequal parts , together with the fquare of the line between the points of fection , is equal to the fquare of half the line . Let the straight line AB be divided into two equal parts in the point C , 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