| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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