| Euclid, Isaac Todhunter - 1883 - 400 Seiten
...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... | |
| 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 Seiten
...IST PART. and the theorem can easily be 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** order, have the same ratio, the first shall have to the last of the first magnitudes the same ratio... | |
| Joseph Battell - 1903
...a glance, and she thinks any one ought to, that 2 : 12 :: 3 : 18. PROPOSITION XXII. ' If there are **any number of magnitudes, and as many others, which, taken two and two in** order, have the same ratio ; the first will have to the last of the first magnitudes, the same ratio... | |
| Euclid - 1908
...as E to F; then A is to D as E to H. Because A, £, C are three magnitudes, and F, G, H other three **which, taken two and two in a cross order, have the same ratio,** by the first case, A is to C as F to H. But C is to D as E is to F ; wherefore again, by the first... | |
| Euclid
...the proof as follows : "Next, let there be four magnitudes A, B, C, D, and other four E, F, G, If, **which, taken two and two in a cross order, have the same ratio,** viz. : A to B as G to £T, B to C as F to G, and C to D as E to F; then A is to D as E to H. Because... | |
| 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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