 | Eucleides - 1860 - 396 pages
...book 5. 18. 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. Proposition E, book 5. 19. Ex ccqitali (sc. distantia), or ex cequo, from equality of distance ; when... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...PROPOSITION E. THEOREM. If four magnitudes be proportional!, they are also proportionals by coif version ; that is, the first is to its excess above the second, as the third to if. excess abtve the fourth. Let AB be to BE, as CD to DF. Then BA shall be to AE, as DC to CF. AEB... | |
 | Euclides - 1860 - 288 pages
...the second, as the excess of the third above the fourth, is to the fourth. 26. By conversion, when the first is to its excess above the second, as the third is to its excess above the fourth. 27. By mixing, when the sum of the first and second is to their... | |
 | Euclides - 1861 - 464 pages
...4 = 10 X 6, an identity; .'. 15:15-10=6^6—4. ie 15 : 5 = 6 : 2. PROP. E. — THEOR. Convertendo. If four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. " If fonr magnitudes be proportional, the first being greater than the second, and the third than the... | |
 | George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...shewn that a — с _ с b^~d~d; whence a — с : b — d : : с : d. PROPOSITION E. " CoNVERTENDO." If four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. a, b, c, d. Let a : b : : с : d. Then shall a : a — b : : с : с — d. Because a : b : : с :... | |
 | Euclides - 1863 - 122 pages
...Book V. XVII. Canvertendo, by «onversion: when there are four proportionals, and il is inferred that the first is to its excess above the second, as the third to its excess above the fourth. XVIII. Ex txguali (sc. distuntid), or ex tcquo, from equality of distance: when there is any number... | |
 | Euclides - 1864 - 448 pages
...Bookv. XVU. 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. XVIII. Ex sequali (so. distantia), or ex sequo, from equality of distance : when there... | |
 | Robert Potts - 1865 - 528 pages
...that taken from the other. The demonstration is contained in the preceding. PROPOSITION E. THEOREM. lf four magnitudes be proportionals, they are also proportionals...second, as the third to its excess above the fourth. Lot AB be to BE, as CD to DF. Then BA shall be to AE, as DC to CF. AEB CFD Because AB is to BE, as... | |
 | Euclides - 1865 - 402 pages
...taken from the other ; the remainder shall be to the remainder as the whole to the whole. Prop. E. If four magnitudes be proportionals, they are also...first is to its excess above the second, as the third 10 its excess above tl e four:I,. Prop. 20. If there be three magnitudes, and other three, which, taken... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 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 cequall distantia, or ex aqua, from equality of distance... | |
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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. 
