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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.
A Supplement to the Elements of Euclid - Page 288
by Daniel Cresswell - 1819 - 410 pages

## Universal Technological Dictionary: Or, Familiar Explanations of ..., Volume 2

George Crabb - Industrial arts - 1823 - 704 pages
...to be BE as CD to EF, then, by division, AE is to EB as CF to FD. Proportion by conversion is when the first is to its excess above the second as the third to its excess above the fourth. — Ordiiiate proportion, or proportion ex a:quali,\.e. from equality of distance, is when any number...

## An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...D and the ratio of rA-A to rB-B,is and therefore rA : rB : : rA— A : rB— B. QED PROP. E. THEOR. 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. DEMONSTRATION. Let rA, A, rB, B, be the four proportionals, we have...

## An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...therefore rA : rB : : rA— A : rB— B. PROP. E. THEOR.~jt-*. If four magnitudes be-proportionals, they are also proportionals by conversion ; that is,...first is to its excess above the second as the third is to its excess above the fourth. DEMONSTRATION. Let rA, A, rB, B, be the four proportionals. we have...

## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...Book 5. XVII. 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 5. XVIII. Ex xquali (se. distentía), or ex tequo, from equality of diittnce; when there...

## An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - Algebra - 1826 - 430 pages
...rrrr^ rrs — D (i — I).D ?—, and therefore D rA: rB : : rA— A: rB— B. QED PROP. E. THEOR. 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. DEMONSTRATION. Let rA, A, rB. B, be the four proportional?, we have...

## Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...a±b'.b:'.c ±d'. <?. 115. Iffour quantities be proportionals, they are also proportionals convertendo, that is, the first is to its excess above the second, as the third to its excess above the fourth. For, since a:b :: c:d, a — b:b::c — d:d, (No. 114.) and, alternately, (No. 112.) a — b: c —...

## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...first to that taken from the other. The demonstration is contained in the preceding. PROP. E. THEOR. If four magnitudes be proportionals, they are also proportionals by conversion : that is, the Jirst is to its excess above the second, as the third to its excess above the fourth. Let AB be to...

## The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...(465) XVIII. 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 V. Conversion consists in substituting the differences of the antecedents A a and...