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" 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 ratio which the first of the others has to the last. NB This is... "
The Elements of Euclid, books i. to vi., with deductions, appendices and ... - Page 276
by Euclides - 1884
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 592 pages
...THEOR. s«oN. IF there be any number of magnitudes, and as many • other, which, taken two and two in order, have the same ratio; the first shall have to...ratio which the first of the others has to the last. NB This is usually fifed by the words " &c tfquali" or, " eiv aqua." F 4. 5. First, Let there be three...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 348 pages
...and as many others, which, taken twoand two, in a cross order, have the same ratio ; the first will have to the last of the first magnitudes the same...three magnitudes, A, B, C, and other three, D, E, and F, which, taken two and two, in a cross order, have the same ratio, viz. A : B : : E : F, and B...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 714 pages
...XXII. Theor. If there be any number of magnitudes, and as many others, which, taken two and t«m in order, have the same ratio ; the first shall have to the last of the flrst magnitudes the same ratio which the first of the others IKIS to the last. NB This is usually...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...and as many others, which, taken twoand two, in a cross order, have the same ratio ; the first will have to the last of the first magnitudes the same ratio which tiie first of the others has to the last.* First, let there be three magnitudes, A, B, C, and other...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 518 pages
...it may be shewn, that, if A be equal to C, 0 is equal to F ? and if less, less. PROP. XXI. THEOR. If there be three magnitudes (A, B, C), and other three (D, E, F), which, taken two and two in aperturbate order, are in the same ratio; if the first (.4), of the jirst...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 548 pages
...XXII. THEOB. 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 rank of magnitudes, the same ratio which the first of the others has to the last. NB This is usually...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...XXII. THEOB. 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 rank of magnitudes, the same ratio which the first of the others has to the last. NB This is usually...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1058 pages
...others, nntch, taken two and two, in a cross order, have the same ratio ; the first shall have to l/¿e last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words, " ex aequali in pi oportione pertúrbala ;" or " ex eequo pertúrbalo."...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1826 - 326 pages
...have the- . same ratio ; the first will have to the last of the first magnitudes the same ratio Whieh the first of the others has to the last.* First, let there be three magnitudes, A, B, C, and othor three, D, E, and F, whieh, taken two and two in a eross order, have the same ratio, viz. A :...
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An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - Algebra - 1826 - 430 pages
...of the proposition may be shown. whatever be the number of magnitudes. QED PROP. Kill. THEOR. tio ; the first shall have to the last of the first magnitudes the sume ratio which the first of the others has to the last. NB This is usually cited by the words ex...
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