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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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 488 pages
...equality of diftance; when there is any number of magnitudes more than two, and as many others, fo that they are proportionals when taken two and two of each rank, and it is inferred, that the firft is to the laft of the firft rank of magnitudes, as the firft is to the laft of the others. '...
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The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ...

Benjamin Donne - Geometry, Plane - 1775 - 338 pages
...Equality of Difiance -, when there is any Number of Magnitudes more than two, and as many others fo that they are Proportionals when taken two and two of each Rank, and it is inferred, that the firft is to the laft of the firft Rank of Magnitudes, as the firft is to the hit of the others. —...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 534 pages
...equality of diftance ; when there is any number of magnitudes more than two, and as many others, fo that they are proportionals when taken two and two of each rank, and it is inferred, that thi firft is to the laft of the firft rank of magnitudes, as the firft ft to the laft of the others...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...equality of diflance ; when there is any number of magnitudes more than two, and as many others, fo that they are proportionals when taken two and two of each rank, and it is inferred, that the firft is to the laft of the fir ft rank of magnitudes, as the fit)'. is to the laft of the others :...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...equality of diftance ; when there is any number of magnitudes. more than two, and as many others, fo that they are proportionals when taken two and two of each rank, and it is inferred, that the firft is to the laft of the firft rank of magnitudes, as the firft is to the laft of the orhers : Of...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 pages
...equality of diftance; when there is any number of magnitudes more than two, and as many others, fo that they are proportionals when taken two and two of each rank, and it is inferred, that the firft is to the laft of the firft rank of magnitudes, as the firft is to the laft of the others. '...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...equality of distance; when there is any пишber 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 iui'erreO, that the first is to the last ot the first rank of magnitudes, As the tirst is to the last...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 pages
...equality of distance ; when there is any Humber of magnitudes more than two, and as many others, so that they are proportionals when taken two and two of each rank, and it it inferred, that the first is to the last of the first rank of magnitudes, as the first is to the...
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Universal Technological Dictionary: Or, Familiar Explanations of ..., Volume 2

George Crabb - Industrial arts - 1823 - 704 pages
...magnitudes more than two are proportionals in such manner, that when taken two and two of each rank, it is inferred that the first is to the last of the...magnitudes as the first is to the last of the others, as in fig. 34, supposing A to be to B as D to E, and B to C as E to F; then, ex cequali, A is to C...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 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 olher rank. XXI. If A, B, C, D, be any number of magnitudes of the...
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