 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...be, &c. QED Recite (a) hyp. ; (4) p. 16, 5 ; (c)p. 17, 5; (d)p. 11, 5. E Th. Of four proportionals, the first is to its excess above the second as the third is to its excess above the fourth. Given AB : BE : : CD : DF ; then, by hyp., AB : AB— BE : : CD... | |
 | 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...second, as the third to its excess above the fourth. PROP. XX. THEOREM. If there be three magnitudes, and other three, which, taken two and two, have the... | |
 | Euclides - Geometry - 1853 - 176 pages
...Book 5. XVII. Converterido, 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 5. XVIII. Ex œquaM (sc. distantia), or ex ceqiw, from equality of distance ; when there... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...Book V. 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 to its excess above the fourth. Prop. E , Book V. 18. Ex sequali (sc. distantia), or ex sequo, from equality of distance; when there... | |
 | 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...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 BE,... | |
 | John Ogilvie - English language - 1855 - 434 pages
...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 by conversion. CONVER'SIVE, a.... | |
 | Euclides - 1855 - 230 pages
...book 6. 18. 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. Proposition E, book 5. 19. Ex ceqwtli (so. digtantia), or ex cgquo, from equality of distance ; when... | |
 | John Playfair - Geometry - 1855 - 334 pages
...Book 5. 18. 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 19. Ex aequali (sc. distantia), or ex sequo, from equality of distance ; when there is any number of... | |
 | 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... | |
 | Noah Webster - English language - 1857 - 1310 pages
...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... | |
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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. 
