 | James Wood - 1857 - 634 σελίδες
...cd that is, —— = ——; b il or a — b : b :: c — d : d. 246. Again, convertendo, the ßrst is to its excess above the second, as the third is to its excess above the fourth. (Еисыо, B. v. Prop. E.) а-Ь c—d By the last Article, d bd and - «= - (Art. 242) ; а с a... | |
 | Eucleides - 1860 - 396 σελίδες
...therefore - 4- 1 = - + 1, AB AA + B therefore = and therefore A:C::A + B:C 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 is to DF ; then AB is to AE, as CD is to CF.... | |
 | Euclides - 1860 - 288 σελίδες
...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 •inu.Mc-nce, as the sum of the third... | |
 | Robert Potts - 1860 - 380 σελίδες
...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.... | |
 | Euclides - 1861 - 464 σελίδες
...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...first is to its excess above the second, as the third to its excess above the fourth. " If fonr magnitudes be proportional, the first being greater than... | |
 | George Sturton Ward - 1862 - 104 σελίδες
...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...first is to its excess above the 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... | |
 | Euclides - 1863 - 122 σελίδες
...preceding. TEOP. E. (THEOBEM).—If Jam magnitudes be proportionals, theg are also proportionals bg 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. And let AE be the excess of AB above I3E,... | |
 | Euclides - 1864 - 448 σελίδες
...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 σελίδες
...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 σελίδες
...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.... | |
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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... 
