The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Seite 46
If a straight line be divided into any two parts , the squares of the whole line , and of one of the parts , are equal to twice the rectangle contained by the whole and that part , together with the square of the other part .
If a straight line be divided into any two parts , the squares of the whole line , and of one of the parts , are equal to twice the rectangle contained by the whole and that part , together with the square of the other part .
Seite 49
If , therefore , a straight line be divided , & c . Q. E. D. Otherwise . - Because BC is divided into any two parts at D , the square of BD , and twice the rectangle BC.CD are together equal ( II . 7 ) to the squares of BC and CD .
If , therefore , a straight line be divided , & c . Q. E. D. Otherwise . - Because BC is divided into any two parts at D , the square of BD , and twice the rectangle BC.CD are together equal ( II . 7 ) to the squares of BC and CD .
Seite 52
In every triangle , the square of the side subtending either of the acute angles , is less than the squares of the sides containing that angle , by twice the rectangle contained by either of these sides , and the straight line ...
In every triangle , the square of the side subtending either of the acute angles , is less than the squares of the sides containing that angle , by twice the rectangle contained by either of these sides , and the straight line ...
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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 |