 | Euclides - 1848 - 52 σελίδες
...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 - 1853 - 400 σελίδες
...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 - 1853 - 176 σελίδες
...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 - 1853 - 334 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | John Ogilvie - 1855 - 434 σελίδες
...COX\'ERS'H)N,n.[add.]Co«rer,.-iono/ proportions, in math., 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, and the four terms, when thus arranged, are said to be proportionals... | |
 | Noble Heath - 1856 - 472 σελίδες
...— y '• x an<^ invertendo P ' P — q '• '• x : x — y ; that is to say, the fi->-st is tn 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... | |
 | Noah Webster - 1857 - 1310 σελίδες
...one. — Conversion of proportion* in mathematics, IB when, of four proportionals, it id inferred that the first is to its excess above the second as the third is to its excess above the fourth. — Conversion of propositions, in logic, is a changing of the subject into the place of the predicate,... | |
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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... 
