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" ... that they are proportionals when taken two and two of each rank, and it is inferred, that the first is to the last of the first rank of magnitudes, as the first is to the last of the others: ' Of this there are the two follow' ing kinds, which arise... "
The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ... - Page 31
by George Sturton Ward - 1862 - 79 pages
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...first rank as the last but two to the last but one of the other rank, and so on in a cross order ; and it is inferred that the first is to the last of the first rank as the first is to the last of the other rank. XXI. If A, B, C, D, be any number of magnitudes of the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...equality of diittnce; when there is any number of magnitudes more than two, and as many others, so that they are proportionals when taken two and two of each rank, and it is inferred, that the first ig to the last of the first rank of magnitudes, as the first is to the last of the others : ' Of this...
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An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - Algebra - 1826 - 430 pages
...equality of distance, when there is any number of magnitudes more than two, and as many others, so that they are proportionals when taken two and two...last of the first rank of magnitudes as the first is t the last of the others : of this there are the two following kinds, which arise from the different...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 548 pages
...from equality of distance when there is any number of magnitudes more than two, and as many others, so that they are proportionals when taken two and two...and it is inferred, that the first is to the last of Ihe first rank of magnitudes, as the first is to the last of the others: 'Of this there are the two...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...equality of distance, when there is any number of magnitudes more than two ; and as many others, so that they are proportionals when taken two and two...the last of the others : ' Of this there are the two fol' lowing kinds, which arise from the different order in which ' the magnitudes are taken two and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...equality of distance, when there is any number of magnitudes more than two; and as many others, so that they are proportionals when taken two and two...the last of the others : ' Of this there are the two fol' lowing kinds, which arise from the different order in which ' the magnitudes are taken two and...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...equality of distance ; when there is any number of rnagni. ludes more than two, and as many others, so that they are proportionals when taken two and two...first is to the last of the first rank of magnitudes, ;is the first is to the last of the others. Of this there are the two following kinds which arise from...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...equality of distance ; when there is any number of magnitudes more than two, and as many others, so that they are proportionals when taken two and two...inferred, that the first is to the last of the first rank ol magnitudes, as the first is to the last of the others ; Of this there are the two following kinds,...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...difference. 28. By equality, when there is any number of magnitudes more than two, and as many others, so that they are proportionals when taken two and two of each rank, and it is inferred — that ihejirst is to the last of the first rank of magnitudes, as fae first is to the last of the others:...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...third to its excess above the fourth. Prop. E. Book 5. XVIII. Ex tequali (sc. distantia), or ex teguo, from equality of distance; when there is any number...the last of the others: ' Of this there are the two follow' ing kinds, which arise from the different order in ' which the magnitudes are taken two and...
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