The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Seite 58
Wherefore AB is bisected at F. Wherefore , if a straight line , & c . Q. E. D. Corollary . If there be any number of parallel chords in a circle , the diameter perpendicular to one of them bisects all of them . Exercise .
Wherefore AB is bisected at F. Wherefore , if a straight line , & c . Q. E. D. Corollary . If there be any number of parallel chords in a circle , the diameter perpendicular to one of them bisects all of them . Exercise .
Seite 148
But G H is similar to E L. There- fore M N is similar to E L. Wherefore E L and M N are about the same diagonal F X. Produce LB to P , and A B to O. The straight line AB is produced to O as re- quired ( IV . 26 ) .
But G H is similar to E L. There- fore M N is similar to E L. Wherefore E L and M N are about the same diagonal F X. Produce LB to P , and A B to O. The straight line AB is produced to O as re- quired ( IV . 26 ) .
Seite 159
Therefore FA and A G are equal to FB and B H , each to each , and the angle FAG has been proved equal to the angle FB H. Wherefore the base G F is equal ( I. 4 ) to the base FH . But it has been proved that G E is equal to EH , and E ...
Therefore FA and A G are equal to FB and B H , each to each , and the angle FAG has been proved equal to the angle FB H. Wherefore the base G F is equal ( I. 4 ) to the base FH . But it has been proved that G E is equal to EH , and E ...
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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 |