 | 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... | |
 | Euclides - 1865 - 402 pages
...to that taken from the other. The demonstration is contained in the preceding. PROP. E.— THEOREM. If four magnitudes be proportionals, they are also...first is to its excess above the second, as the third to its excess above the fourth. (References— Prop. v. B, 17, 18.) Let AB be to BE, as CD to DF. Then... | |
 | 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...first is to its excess above the 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.... | |
 | 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 ; when there is any number of magnitudes... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...magnitudes be proportionals, they shall also be proportionals by conversion; that is, the first shall be to its excess above the second as the third is to its excess above the fourth. Let AB be to BE as CD is to DF: AB shall be to AE as CD is to CF. For, because AB is to BE as CD is... | |
 | Robert Potts - 1868 - 434 pages
...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... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...magnitudes be proportionals, they must also be proportionals by conversion ; that is, the first must be to its excess above the second as the third is to its excess above the fourth. Let A, B together be to B as C, D together is to D. Then must A, B together be to A as C, D together... | |
 | Euclides - 1874 - 342 pages
...taken from the other. The demonstration is contained in the preceding. PROPOSITION E. — Theorem. If four magnitudes be proportionals, they are also...first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF. Then BA shall be to AE, as DC to CF.... | |
 | Charles Lutwidge Dodgson - 1874 - 96 pages
...fourth. (Рвор. xvii.) XVII. Convertendo ; 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. (Ркор. Д.) XVIII. Ex sequali; when there is any number of magnitudes... | |
 | Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...fourth. (Рвор. xvii.) XVII. Convertendo ; 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.) XVIII. Ex sequali; when there is any number of magnitudes... | |
| |
THEOB.—If four magnitudes be proportionals, they are also proportionals by conversion; that is, the first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF: then BA shall be to AE, as DC to... 
