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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 Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...and as many others, which, taken two and two, in a cross order, have the same ratio; the first will have to the last of the first magnitudes the same...ratio which the first of the others has to the last. XXIV. If the first has to the second the same ratio which the third has to the fourth ; and the fifth...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...and as many others, which, taken two and two, in a cross order, have the same ratio; the first will have to the last of the first magnitudes the same...ratio which the first of the others has to the last *. ' ' \ ' 1?irst, let there be three magnitudes, A, B, C, and other three, D, E, and F, which, taken...
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Elements of Plane Geometry According to Euclid

Andrew Bell, Robert Simson - Euclid's Elements - 1837 - 290 pages
...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...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 ; namely, A : B : : E : F, and...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...magnitudes, and as many others, which, taken two ana two in order, have the same ratio ; the first will have to the last of the first magnitudes, the same ratio which the first of the other has to the last. First, let there be three magnitudes, A, B, C, and other three, D, E, F, which,...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...than two, and as many others, which, taken two and two in order, have the same ratio ; the first has to the last of the first magnitudes the same ratio which the first has to the last of the others. NB This is usually cited by the words "ex cequo," or " ex ceguali" First,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...THEOR. 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...ratio which the first of the others has to the last. NB This is usually cited by the words " ex aequali in proportione perturbata ;" or, " ex sequo perturbata."*...
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The Elements of Euclid

Euclid - Geometry - 1838 - 468 pages
...THEOR. 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 jatio which the first of the others has to the last. NB This is usually cited by the words " ex sequali...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...the first series of magnitudes the same ratio which the first has to the last of the other series. First, let there be 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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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Euclid's Elements - 1841 - 144 pages
...PROP. XXII. THEO. 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...ratio which the first of the others has to the last of the same. NB — This is usually cited by the words " ex œquali," or " ex œquo." First, let there...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...XXII. THEOR. 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...of the first magnitudes, the same ratio which the fi'..*t has to th . last of the others. N. 13. This is usually cited by the words " ex aequali," or...
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