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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 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 oi 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 Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 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 Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1846 - 334 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 oi magnitudes, as the first is to the last of the others ; Of this there are the two following kinds,...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...to its excess above the fourth. — Prop E. Book V. XVIII. Ex œquali (se. distanti‚], or ex œquo, from equality of distance : when there is any number...magnitudes, as the first is to the last of the others : " Uf this there are the two following kinds, which arise from the different order in which the magnitudes...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 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...is to the last of the first rank of magnitudes, as theirs* is to the last of the others : — of this there are the two following kinds, which arise from...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...distance; when there is any number of magnitudes more than two. and as many others such that they arc proportionals when taken two and two of each rank...the last of the others. Of this there are the two kinds, in definitions 19 and 20, which arise from the different order in which the magnitudes are taken...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...txguali (sc. distuntid), or ex tcquo, from equality of distance: when there is any number of magnitndes more than two, and as many others, such that they...that the first is to the last of the first rank of magnitndes, as the first is to the last of the others. "Of this there are the two following kinds,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...the second, as the third is to its excess above the fourth. VE 18. Ex cequall distantia, or ex aqua, from equality of distance ; when there is any number...first is to the last of the others. Of this there arc the two following kinds, which arke from the different order in which the magnitudes are taken,...
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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
...the second, as the third is to its excess above the fourth. VE 18. Ex ccquali distantia, or ex cequo, from equality of distance; when there is any number...two and two of each rank, and it is inferred, that tho first is to the last of the first rank of magnitudes, as the first is to the last of the others....
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...equality of distance ; used when there is any number of magnitudes more than two and as many others so that they are proportionals when taken two and two...is to the last of the others. Of this there are the following two kinds which arise from the different order in which the magnitudes are taken, two and...
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