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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... "
An Elementary Treatise on Algebra, Theoretical and Practical ... - Σελίδα 352
των James Ryan, Robert Adrain - 1835 - 361 σελίδες
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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...taken from the first to that taken from the other : the demonstration is contained in the preceding;. B PROP. E. THEOR. IF four magnitudes be proportionals,...first is to its excess above the 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...

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

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...: 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...first is to its excess above the second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : A— B : : C : C— D. For,...

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

Euclid - 1810 - 518 σελίδες
...is contained in the preceding. PROP. E. THEOR, IF four magnitudes be proportionals, they are als« 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 is to AE, as DC to CF. Because...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...magnitude taken from the other; the remainder shall be to the remainder, as the whole to the whole. Prop. E. Theor. If four magnitudes be proportionals,...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...

Easy Introduction to Mathematics, Τόμος 2

Charles Butler - 1814
...— — , 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,...

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

Euclides - 1816 - 528 σελίδες
...taken from the first to that taken from the other : The demonstration is contained in the preceding. . PROP. E. THEOR. IF four magnitudes be 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 to DF; then BA istoAE, as DC to CF. Because...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 σελίδες
...but A : B : : fore (11. 5.) AC : BD : : A : B. Therefore, &c. Q, ED COR. AC : BD ::C.: D. PROP. D. THEOR. If four magnitudes be proportionals, they are...first is to its excess above the second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : AB : : C : CD. For, since A...

A Supplement to the Elements of Euclid

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...shewn that A : B : : A— B : B— C ; And .(%>.) A>B; .-. (S. 1. 5.) AB>BC. PROP. XVI. 18. 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 A+B : B : : C + D : D ; then A+B : A : : C+D:C. For (dividendo)...

Elements of Geometry

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...the fourth is to the fourth ; convertendo, by conversion, when it is inferred that the first is to iU excess above the second, as the third is to its excess above the fourth. VI. When a proportion is said to exist among certain magnitudes, these magnitudes are supposed to be...

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

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...Books. 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. Prop. D. Book 5. XIX. Ex aaquali (sc. distantia), or ex aequo, from...




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