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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... "
Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Seite 217
von Euclides - 1861
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

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...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

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...
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The Harpur Euclid: An Edition of Euclid's Elements

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...
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Ellen: Or, Whisperings of an Old Pine, Band 1

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...
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Books 3-9

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...
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The Thirteen Books of Euclid's Elements

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...
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Pass school, group A (-D).

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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