| Isaac Todhunter - 1880 - 400 sider
...is greater oD; t is, D is less than F. Wherefore, if there be three &c. QED PROPOSITION 22. THEOREM. **If there be any number of magnitudes, and as many others, which** have the same ratio, taken two and two in order, the first shall fiave to the last of the first magnitudes... | |
| Euclides - 1881
...* ex aquali," or * ex ayuo," that it, from equality of distance U'ff. \9). PROP. XXIII. THEOREM. y **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 shatt havt to the last of the first magnitudes the same... | |
| Euclid, Isaac Todhunter - 1883 - 400 sider
...is, D is less than F. AB PE C F AB D B B I EUCLID'S ELEMENTS DE I GKMHL 1ST PROPOSITION 22. THEOREM. **If there be any number of magnitudes, and as many others, which** have the same ratio, taken two and two in order, the first shall have to the last of the first magnitudes... | |
| Henry William Watson - 1884
...times the sum A+C+E is equal to m times the sum B + D + F, therefore ± is equal to , PROPOSITION 12. **If there be any number of magnitudes, and as many...taken two and two in order have the same ratio, the** Jirst shall have to the last of the first set of magnitudes the same ratio as the first has to the... | |
| Euclides - 1884
...BV 13 Now C:B = E:D; .-. E: F is less than E:D; F. 13 D is less than FF 10 PROPOSITION 22. THEOREM. **If there be any number of magnitudes, and as many others, which taken two and two in** direct order, have the same ratio ; tJie first shall have to the last of the first magnitudes the same... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...[IST PART. and the theorem can be easily extended to any number of magnitudes. Hence generally : — **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... | |
| Joseph Battell - 1903
...which the first of the others has to the last.' " See Proposition XX. PROPOSITION XXIII. ' If there are **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... | |
| Euclid - 1908
...P." He also gives the extension of the proposition to any number of magnitudes, enunciating it thus : **"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... | |
| Euclid
...He also gives the extension of the proposition to any number of magnitudes, enunciating it thus : " **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... | |
| Oxford univ, exam. papers, 2nd publ. exam - 1884
...rectilineal figure and equal to another given rectilineal figure. 8. Inscribe a square in a given circle. 9. **If there be any number of magnitudes, and as many others, which** have the same ratio, taken two and two in a cross order, the first shall have to the last of the first... | |
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