Books Books
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

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

Robert Simson - Trigonometry - 1806 - 546 pages
...to that taken from the other : the demonstration is contained in the preceding;. B PROP. E. THEOR. IF four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. a 17. 5. bB.5. c 18. 5. See N. Let AB be to BE as CD to DF ; then BA is to AE as DC to CF. Because...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...: B. Therefore, &c. QE D, COR. A— C : B— D : : C : D. PROP. D. THEOR. a 17. 5. b A. 5. c 18. 5. IF four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : A— B : : C : C— D. For, since A : B : : C : D, by division1,...

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 554 pages
...is contained in the preceding. PROP. E. THEOR, IF four magnitudes be proportionals, they are als« proportionals by conversion, that is, the first is...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 to CF. Because AB is to BE, as CD to DF, by divia 17....

## Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...from the other; the remainder shall be to the remainder, as the whole to the whole. Prop. E. Theor. If four magnitudes be proportionals, they are also...proportionals by conversion, that is, the first is to its exciss above the second, as the third to its excess above the fourth. Prop. XX. Theor. If there he...

## The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 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...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 to CF. Because AB is to BE, as CD to DF, by di' 17....

## Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814 - 582 pages
...— — , that is, a—b:b::c—d:d; thii is called 01 viha DESDO. Euclid 17, 5. 68. In like manner, the first is to its excess above the 'second, as the third to its excess above the fourth. a— b c—d , , ,. , . bd Because — ; — = — - — by the preceding, and since — = — , odac...

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...; when there are four proportionals, and it is inferred, that the first Is to its excess I B6on V. above the second, as the third to its excess above the ' — ^ fourth. Prop. E. Books. XVIII. Ex aequali (sc. distantia), or, ex aequo, from equality of distance ; when there...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...there fore (11. 5.) AC : B- D : : A : B. Therefore, &c. QE D, COR. AC : BD : : C : D. PROP. D. THEOR. If four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : AB : : C : C -D. For, since A : B : : C : D, by division (17....