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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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...Te any number of magnitudes, and as many othert, which laTcen two and two in order, have the satne ratio ; the first shall have 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 eequali," or " ex sequo."...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...less. Prop. 22. 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 ra'io which the first has to the last of the others. NB This is usually cited by the words ' ex gequali,'...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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...ratio which the first of the others has to the last. [This proposition is usually cited by the words ex aguali.] First, let there be three magnitudes A,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...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 the same ratio ichich the first of the others has to the last. [This proposition is usually cited by the worda ex...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...XXII. THEOREM. If there be any number of magnitudes, and a3 many others, which taken two and two in order, have the same ratio ; the first shall have...the first magnitudes, the same ratio which the first has to the last of the others. NB 'Ihib is usually cited by the words " ex sequali," or " ex aequo."...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...PROPOSITION 12. 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 set of magnitudes the same ratio as the first has to the last of the second set of magnitudes. Fig....
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...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 the same...ratio which the first of the others has to the last of these. First, let there be three magnitudes A, B, C, and other three D, E, F. And let A be to B...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 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...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 sequali in proportione perturbatS...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...XXII. THEOKEM. 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...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 sequali," or " ex 'tequo."...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879 - 414 pages
...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 magnitudes...ratio which the first of the others has to the last. 10. Equal triangles which have one angle of the one equal to one angle of the other, have tneir sides...
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