| John Playfair - Euclid's Elements - 1849 - 332 pages
...and B : A : : F : E, therefore, by this first case, since CyA, F7 D, that is, D/F. PROP. XXII. THEOR. **If there be any number of magnitudes, and as many others, which, taken two** ana two in order, have the same ratio ; the first will have to the last of the first magnitudes, the... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...less than F. Therefore, if there be three, etc. QED c • EUCLID S ELEMENTS. PROPOSITION XXII. THEOR. **If there be any number of magnitudes, and as many...which, taken two and two in order, have the same ratio** ; the first shall have to the last of the first magnitudes, the same ratio which the first of tke others... | |
| Euclides - 1853 - 176 pages
...number of magnitudes. Therefore, if there be any number, <fec. QED PROPOSITION XXIII. — THEOREM. **If there be any number of magnitudes, and as many others, which, taken two and two, in** a cross order, have the same ratio ; the, first sliall have to the last of the first magnitudes the... | |
| John Playfair - Euclid's Elements - 1855 - 340 pages
...demonstration extended to any number of magnitudes. nF(11.5.). Again, PROP. XXIII THEOR. If there le **any number of magnitudes, and as many others, which, taken two and two, in** a cross order, have the same ratio ; the first will have to the last of the first magnitudes the same... | |
| Euclides - 1855 - 262 pages
...Therefore, if there be three, &c. QED PROP. XXII. THEOREM. If there be any number of magnitudes, andas **many others, which taken two and two in order, have the same ratio** ; (he first shall have to the last of the first magnitudes, the same ratio which the first has to the... | |
| Euclides - 1855 - 230 pages
...3 KMHLN ABC_EFG lhen B ' C ' DF ' G ' H' therefore A : D :: E : H. PROPOSITION XXIII. THEOREM.—Jf **there be any number of magnitudes, and as many others, which, taken** tivo and two, in a cross order, have tlie same ratio; the first has to the last of the first magnitudes... | |
| Euclides - 1859 - 136 pages
...laa rо irXqöOç, aiivSvo \apßavoptva Kai iv rif avrif \oyif Kai Stîffov iv ry avru Xóyy Éffrai. **If there be any number of magnitudes, and as many others, which, taken two and two,** have the same ratio; they shall be in the same ratio by equality. Statement — Let there be three... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...first; that is, JD is less than JP. Therefore, if there be three, &c. QED PROPOSITION XXII. THEOREM. **If there be any number of magnitudes, and as many...which taken two and two in order, have the same ratio** ; the first shall have to the last of the first magnitudes, the same ratio which the first has to the... | |
| Eucleides - 1860 - 396 pages
...any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio. **If there be any number of magnitudes, and as many others, which, taken two and two, in** a cross order, have the same ratio. If magnitudes are equal . . If two magnitudes are unequal. If a... | |
| Euclides - 1860 - 288 pages
...same manner the demonstration is extended to any number of magnitudes. PROPOSITION XXIII. THEOREM. **If there be any number of magnitudes, and as many others, which, taken two and two in** a cross order, have the same ratio ; the first shall have to the last of the first magnitudes the same... | |
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