 | Euclides - 1881 - 236 σελίδες
...* 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,...in a cross order, have the same ratio ; the first shatt havt to the last of the first magnitudes the same ratio which the first hat to the last of the... | |
 | Euclid, Isaac Todhunter - 1883 - 428 σελίδες
...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 - 434 σελίδες
...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 - 538 σελίδες
...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 - 722 σελίδες
...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 - 456 σελίδες
...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 - 452 σελίδες
...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 - 594 σελίδες
...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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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 which the first of the others has to the last. NB This is usually... 
