The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Seite 58
If a straight line cut the circumferences of two concentric circles , the segments intercepted between the circles are equal . PROP . IV . THEOREM . If in a circle two straight lines cut one another , and do not pass through the centre ...
If a straight line cut the circumferences of two concentric circles , the segments intercepted between the circles are equal . PROP . IV . THEOREM . If in a circle two straight lines cut one another , and do not pass through the centre ...
Seite 63
H Therefore the straight line which joins the centres of the circles ADE and A B C , being produced , cannot pass otherwise than through the point A ; that is , it must pass through the point A. Therefore , if one circle , & c .
H Therefore the straight line which joins the centres of the circles ADE and A B C , being produced , cannot pass otherwise than through the point A ; that is , it must pass through the point A. Therefore , if one circle , & c .
Seite 79
First , let A C and BD pass each through the centre E. Because the segments A E , E C , B E and ED are all equal ( I. Def . 15 ) . There- fore the rectangle A E.E C , is equal to the rectangle BE.ED. Secondly , let the one BD pass ...
First , let A C and BD pass each through the centre E. Because the segments A E , E C , B E and ED are all equal ( I. Def . 15 ) . There- fore the rectangle A E.E C , is equal to the rectangle BE.ED. Secondly , let the one BD pass ...
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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 |