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 119
... excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . 17th Prop . book 5 . XVII . Convertendo , by conversion ; when there are four proportionals , and it * See Note ...
... excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . 17th Prop . book 5 . XVII . Convertendo , by conversion ; when there are four proportionals , and it * See Note ...
Side 120
... excess above the fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance when there is any number of magnitudes more than two , and as many others , so that they are proportionals when ...
... excess above the fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance when there is any number of magnitudes more than two , and as many others , so that they are proportionals when ...
Side 142
... excess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. Because AB is to BE , as CD to DF , by divi- sion ( 17. 5. ) , AE is to EB , as CF to FD , and by ...
... excess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. Because AB is to BE , as CD to DF , by divi- sion ( 17. 5. ) , AE is to EB , as CF to FD , and by ...
Side 148
... excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The demon- stration of this is the same with that of the proposition , if divi- sion be used instead of composition . COR . 2 ...
... excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The demon- stration of this is the same with that of the proposition , if divi- sion be used instead of composition . COR . 2 ...
Side 184
... excess of EF above C , and similar and similarly situated to D ; but D is similar to EF , therefore ( 21. 6. ) also KM is similar to EF ; let KL * See Note : be the homologous side to EG , and LM , 184 BOOK VI . THE ELEMENTS OF EUCLID .
... excess of EF above C , and similar and similarly situated to D ; but D is similar to EF , therefore ( 21. 6. ) also KM is similar to EF ; let KL * See Note : be the homologous side to EG , and LM , 184 BOOK VI . THE ELEMENTS OF EUCLID .
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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