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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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...first to that taken from the other. The demonstration is contained in the preceding. PROPOSITION E. THEOREM. If four magnitudes be proportionals, they are also proportionals by conversion ; that is, Ike first is to ill excess above the second, as the third to its excess above the fourth. Let AB be...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 pages
...there be four magnitudes proportional, but the first be greater than the second, the first will be to its excess above the second, as the third to its excess above the fourth. COR. 2. — If there be four magnitudes proportional, A to B as C to D, the difference between the...
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Euclid, book v. proved algebraically, so far as it relates to commensurable ...

Charles Lutwidge Dodgson - 1874 - 96 pages
...taken from the other.] The Demonstration is the same as in the Proposition. PBOP. E. (Convertendo.) If four magnitudes be proportionals : they are also...first is to its excess above the second as the third is to its excess above the fourth. [If four magnitudes (a, Ь, с, d) be proportionals : they are also...
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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
...taken from the other.] The Demonstration is tlte same as in tfo Proposition. T PROP. E. (Convertendo.) If four magnitudes be proportionals : they are also...first is to its excess above the second as the third is to its excess above the fourth. [If four magnitudes (a, b, c, d) be proportionals : they are also...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...Book V. 17. 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. Prop. E. Book V. 18. Ex aequali (so. distantia), or ex aequo, from equality of distance ; when there...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...the second, as the excess of the third above the fourth to the fourth. e. By conversion; the first to its excess above the second, as the third to its excess above the fourth. f. By equality; when there are two ranks of magnitudes, such that, when taken two and two in direct...
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The Elements of Euclid, with Many Additional Propositions and Explanatory ...

Euclid - 1876 - 240 pages
...therefore — + 1 = -+1, AG , A 15 aml— = —; AA therefore = and therefore A:C::A PROPOSITION E. THEOREM. — If four magnitudes be proportionals,...as the third to its excess above the fourth. Let AB be to BE, as CD is to DF ; then AB is to AE, as CD is to CF. DEMONSTRATION. Because AB is to BE, as...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...Book v. XVIL 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. Prop. E. Book v. xvm. Ex aequali (sc. distantia), or ex sequo, from equality of distance : when there...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...V. 17. 17. 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 is to its excess above the fourth. VE 18. Ex cequali distantia, or ex cequo, from equality of distance...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - Euclid's Elements - 1881 - 236 pages
...THEOREM. if four magnitudes be proportional!, they are aIso proportionals by conversion ; that it, the first is to its excess above the second, as the third to its exeat above the fourth. Let AB be to BE, as CD to D F. And let AE be the excess of AB above BE, and...
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