The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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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 ) .
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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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LEMMA I. If from the greater of two unequal magnitudes of the same kind , there be taken more than its half , and from the remainder more than its half ; and so on : there will at length remain a magnitude less than the least of the ...
LEMMA I. If from the greater of two unequal magnitudes of the same kind , there be taken more than its half , and from the remainder more than its half ; and so on : there will at length remain a magnitude less than the least of the ...
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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 touch 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 |