| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...is greater than FV 9. Similarly the other cases may bo proved. Q. nn PROPOSITION XXI. (Eucl. v. 22.) **If there be any number of magnitudes, and as many others, which** have the same ratio taken two and two in order, the first must have to the last of the first magnitudes... | |
| Euclides - 1874 - 342 pages
...be the number of magnitudes. Therefore, if there be any number, &o. QED PROPOSITION 23. — 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... | |
| Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 234 pages
...proportion will be B+A:BA::D + C:DG PHOP. XI.— THEOREM. (Euc. V. 22, 23). Tf there be three or more **magnitudes, and as many others which, taken two and two in order, have the same ratio, then** by equality, the first IMS to the last of the first rank the same ratio that the first has to the last... | |
| Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...> l ; С .-. , xn« by с, а>с. Similarly, if А=С, а=с; and if А<С, а< с. QED PROP. XXII. **If there be any number of magnitudes, and as many others which, taken two and two,** have the same ratio : the first of the first rank shall have to the last the same ratio as the first... | |
| Charles Lutwidge Dodgson - 1874 - 96 pages
....•. , substituting, - > 1 ; QED by c, a>c. Similarly, if A=C, a — c; and if A<C, a< c. PROP. XXII. **If there be any number of magnitudes, and as many others which, taken two and two,** have the same ratio : the first of the first rank shall have to the last the same ratio as the first... | |
| Robert Potts - Geometry, Plane - 1876 - 446 pages
...first; that is, 1) is less than F. Therefore, if there be three, Sic. QED, PROPOSITION XXII. THEOKEM. **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... | |
| University of Oxford - Greek language - 1879 - 412 pages
...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... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...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 - Euclid's Elements - 1881 - 236 pages
...* 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 - Euclid's Elements - 1883 - 426 pages
...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... | |
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