The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Seite 103
third , is of D the fourth ; and of A and C let equimultiples E F and GH be taken . EF is the same multiple of B , that GH is of D. Divide EF into the magni- tudes EK and K F , each equal to A ; and GH into GL and L H , each equal to C.
third , is of D the fourth ; and of A and C let equimultiples E F and GH be taken . EF is the same multiple of B , that GH is of D. Divide EF into the magni- tudes EK and K F , each equal to A ; and GH into GL and L H , each equal to C.
Seite 104
and of A and C certain equimultiples have been taken , -viz . , K and L ; and of B and D certain equimultiples G and H. Therefore , if K be greater than G , L is greater than H ; if equal , equal ; and if less , less ( V. Def . 5 ) .
and of A and C certain equimultiples have been taken , -viz . , K and L ; and of B and D certain equimultiples G and H. Therefore , if K be greater than G , L is greater than H ; if equal , equal ; and if less , less ( V. Def . 5 ) .
Seite 118
A.B.C.D. Because A , B , and C are three magnitudes , and E , F , and G other three , which taken two and two , have the same ratio . Therefore , by the foregoing case , A is to C , as E is to G. But C is to D , as G is to H. Therefore ...
A.B.C.D. Because A , B , and C are three magnitudes , and E , F , and G other three , which taken two and two , have the same ratio . Therefore , by the foregoing case , A is to C , as E is to G. But C is to D , as G is to H. Therefore ...
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A B C ABCD altitude applied base bisected Book Cassell's centre circle circumference cloth coincide common cone Const contained Corollary cylinder definition demonstration described diagonal diameter divided double draw Edition equal equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half Illustrated inscribed interior join less magnitudes manner meet multiple parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proportionals proposition proved pyramid ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle sphere square straight lines A B taken THEOREM third triangle triangle ABC twice vertex Vols Wherefore whole
Bibliografische Informationen
| Titel | The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid Cassell's edition of Euclid Cassell's educational works |
| Autor/in | Euclid |
| Ausgabe | 82 |
| Verlag | Cassell, Petter, and Galpin, 1859 |
| Länge | 212 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |