| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 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 (equali distantia, or ex cequo, from equality of distance... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...17. ' Convertendo,' by conversion ; used 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. It is demonstrated in ' V. E ' that if A+ B : B : : C+ D : D, then... | |
| Euclid - Mathematics, Greek - 1908 - 456 pages
...Proposition E (containing a proof already given by Clavius), on Props. 17 and 18. Prop. E is as follows. **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. Let AB be to BE as CD to DF: then BA is to AE as DC to CF. Because... | |
| Euclid - 452 pages
...Proposition £ (containing a proof already given by Clavius), on Props. 17 and 18. Prop. E is as follows. **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. Let AB be to BE as CD to DF: then BA is to AE as DC to CF. Because... | |
| |