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" If magnitudes, taken jointly, be proportionals, they shall also be proportionals when taken separately: that is, if two magnitudes together have to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall... "
The Elements of Mathematical Analysis, Abridged: For the Use of Students ... - Page 23
by Nicolas Vilant - 1798 - 170 pages
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...magnitudes, taken jointly, be proportionals, they shall also be proportionals when taken separately ; that is, if two magnitudes together have to one of them the same ratio which two others have to one of these, the remaining onai K E. (o) V. 1. f I) V. 2. (c)...
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The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...magnitudes, taken jointly, be proportionals, they shall also be proportionals when taken separately ; that is, if two magnitudes together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...magnitudes, taken jointly, le proportionals, they shall also be proportionals when taken separately : that is, if two magnitudes together have to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...magnitudes, tahen jointly, be proportionals, they shall also be proportionals when tahen separately; that is, if two magnitudes together have to one of them, the same ratio which two others have to one of tliese ; tlien the remaining one of the first two shall...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...magnitudes, taken jointly, be proportional*, they shall also be proportionals when taken separately : that is, if two magnitudes together have to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to...
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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, taken jointly, be proportionals, they shall also be proportionals when taken separately ; that is, if two magnitudes together have to one of them the same ratio which two others have to one of these, the remaining one of the first two must have to the...
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Euclid, book v. proved algebraically, so far as it relates to commensurable ...

Charles Lutwidge Dodgson - 1874 - 96 pages
...four magnitudes, taken jointly, be proportionals : they are also proportionals when taken separately. That is — If two magnitudes together have to one of them the same ratio as two others together have to one of them : the remaining one of the first two has to the...
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Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...four magnitudes, taken jointly, be proportionals : they are also proportionals when taken separately. That is — If two magnitudes together have to one of them the same ratio as two others together have to one of them : the remaining one of the first two has to the...
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