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" Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth. "
A Supplement to the Elements of Euclid - Page 288
by Daniel Cresswell - 1819 - 410 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...to that taken from the other : the demonstration is contained in the preceding;. B PROP. E. THEOR. IF four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. a 17. 5. bB.5. c 18. 5. See N. Let AB be to BE as CD to DF ; then BA is to AE as DC to CF. Because...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...: B. Therefore, &c. QE D, COR. A— C : B— D : : C : D. PROP. D. THEOR. a 17. 5. b A. 5. c 18. 5. IF four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : A— B : : C : C— D. For, since A : B : : C : D, by division1,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 518 pages
...is contained in the preceding. PROP. E. THEOR, IF four magnitudes be proportionals, they are als« proportionals by conversion, that is, the first is...as the third to its excess above the fourth. Let AB be to BE, as CD to DF ; then BA is to AE, as DC to CF. Because AB is to BE, as CD to DF, by divia 17....
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 722 pages
...from the other; the remainder shall be to the remainder, as the whole to the whole. Prop. E. Theor. If four magnitudes be proportionals, they are also...proportionals by conversion, that is, the first is to its exciss above the second, as the third to its excess above the fourth. Prop. XX. Theor. If there he...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...first to that taken from the other: The demonstration is contained in the preceding. PROP. E. THEOR. IF four magnitudes be proportionals, they are also...as the third to its excess above the fourth. Let AB be to BE, as CD to DF; then BA is to AE, as DC to CF. Because AB is to BE, as CD to DF, by di' 17....
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814 - 568 pages
...— — , that is, a—b:b::c—d:d; thii is called 01 viha DESDO. Euclid 17, 5. 68. In like manner, the first is to its excess above the 'second, as the third to its excess above the fourth. a— b c—d , , ,. , . bd Because — ; — = — - — by the preceding, and since — = — , odac...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...; when there are four proportionals, and it is inferred, that the first Is to its excess I B6on V. above the second, as the third to its excess above the ' — ^ fourth. Prop. E. Books. XVIII. Ex aequali (sc. distantia), or, ex aequo, from equality of distance ; when there...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...there fore (11. 5.) AC : B- D : : A : B. Therefore, &c. QE D, COR. AC : BD : : C : D. PROP. D. THEOR. If four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : AB : : C : C -D. For, since A : B : : C : D, by division (17....
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 740 pages
...Theor. If four magnitudes he proportional«, they are also proportionals by conversion, that is, i liv first is to its excess above the second, as the third to its excess above the fourth. Prop. XX. Theor. If there be three magnitudes, and other three, which, taken two and two, have the...
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The First Six Books with Notes

Euclid - 1822 - 179 pages
...be proved, that if there be four magnitudes proportional, and the first be greater than the second, the first is to its excess above the second, as the third to its excess above the fourth. Cor. 2. If there be four magnitudes proportional, AF,g, 34. to B as C to D ; the difference between...
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