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 CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 49
... rectangle contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let BC be divided into any parts in the ...
... rectangle contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let BC be divided into any parts in the ...
Side 50
... rectangle contained by A , BD , together with that contained by A , DE , and that contained by A , EC ... rectangle BH is equal to the rectangles BK , DL , EH ; and BH is contained by A , BC , for it is contained by GB , BC , and GB is ...
... rectangle contained by A , BD , together with that contained by A , DE , and that contained by A , EC ... rectangle BH is equal to the rectangles BK , DL , EH ; and BH is contained by A , BC , for it is contained by GB , BC , and GB is ...
Side 51
... rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the square of AB . If therefore a straight line , & c . Q. E. D. PROP . III . THEOR . Ir a straight line be divided into any two parts , the rectangle ...
... rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the square of AB . If therefore a straight line , & c . Q. E. D. PROP . III . THEOR . Ir a straight line be divided into any two parts , the rectangle ...
Side 52
... rectangle con- tained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB ; and HF , CK are the squares of AC , CB : wherefore the four ...
... rectangle con- tained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB ; and HF , CK are the squares of AC , CB : wherefore the four ...
Side 53
... rectangle contained by AD , DB , for DH is equal ( Cor . 4. 2. ) to DB , and E G F DF together with CH is the gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( 43. 1 ...
... rectangle contained by AD , DB , for DH is equal ( Cor . 4. 2. ) to DB , and E G F DF together with CH is the gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( 43. 1 ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore