 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...-C:BD:: A: D. COR. AC : BD : : C : D. PROP. D. THEOR. If four magnitudes be proportionals, they arc also proportionals by conversion, that is, the first is to its excess above the second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : A— B : : C : C— D. For,... | |
 | Euclides - 1846 - 292 pages
...17) : xvn. 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 (S. E) : XVIII. Ex tequali (sc. distantia), or ex cequo, from equality... | |
 | W. M. Buchanan - Science - 1846 - 768 pages
...vertor, to be turned. CONVER'SION (of proportion), is when, of four proportionals, It is inferred that the first is to its excess above the second, as the third to its excess above the fourth. 2. In logic, a proposition is said to be converted when the terms are... | |
 | Euclides - 1848 - 52 pages
...remainder, as the magnitude taken from the first to that taken from the other. PROP. E. THEOREM. Ilf 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. PROP. XX. THEOREM. If there be three magnitudes, and other three, which,... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...the first to that taken from the other. The demonstration is contained in the preceding. PROPOSITION E. THEOR. If four magnitudes be proportionals, they...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 is to AE, as DC toCF. Because... | |
 | Euclides - Geometry - 1853 - 176 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 is to ae, as dc tocf. Because... | |
 | Euclides - Geometry - 1853 - 334 pages
...proportional, the first being greater than the second, and the third than the fourth : then the first shall be to its excess above the second, as the third is to its excess above the fourth. OBS. This prop" is usually cited by the word " convertendo." Let AB be to BE as CD is to DP ; AB being... | |
 | Euclides - 1855 - 270 pages
...first is to the part of the second. The demonstration is contained in the preceding. PKOP. E. THKOE.EM. If four magnitudes be proportionals, they are also...first is to its excess above the second, as the third to Us etccesi above the fourth. Let AB be to BE, as CD to D F. And let AE be the excess of AB above... | |
 | Euclides - 1855 - 230 pages
...AB and- = -; therefore = -, , , A A+B and therefore A:C::A + B:C + D. PROPOSITION E. THEOREM.—If 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. Let AB be to BE, as CD is to DF ; then AB is to AE, as CD is toCF.... | |
 | Noble Heath - 1855 - 468 pages
...P — 1 ,• P • • x — y ,• x an<^ invertendo p : p — q : : x : x — y ; that is to say, the first is to its excess above the second, as the third is to its excess above the fourth. 413. If we put the proportion p : q. : : x : y in equation, thus : — = — , because (397) the equality... | |
| |
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... 
