The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Seite 46
But the rect- angle N B.BD and the square of CB is equal ( II . 5 ) to the square of CD . And it has been proved that A D is equal to N B. Therefore the rectangle A D.D B , and the square of CB is equal to the square of CD . PROP .
But the rect- angle N B.BD and the square of CB is equal ( II . 5 ) to the square of CD . And it has been proved that A D is equal to N B. Therefore the rectangle A D.D B , and the square of CB is equal to the square of CD . PROP .
Seite 48
Produce A B to D making B D equal to B C. Because the square of CD is equal ( II . 4 Cor . 2 ) to four times the square of CB ; and twice the rectangle AC . C D is equal ( II . Ax . 2 ) to four times the rectangle A C. C B. Therefore ...
Produce A B to D making B D equal to B C. Because the square of CD is equal ( II . 4 Cor . 2 ) to four times the square of CB ; and twice the rectangle AC . C D is equal ( II . Ax . 2 ) to four times the rectangle A C. C B. Therefore ...
Seite 50
Because E C is equal to CA , the square of E C is equal to the square of CA. Therefore the squares of EC and CA are double of the square of CA. But the square of E A is equal ( I. 47 ) to the squares of EC and CA. Therefore the square ...
Because E C is equal to CA , the square of E C is equal to the square of CA. Therefore the squares of EC and CA are double of the square of CA. But the square of E A is equal ( I. 47 ) to the squares of EC and CA. Therefore the square ...
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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 |