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" IF magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together... "
A Treatise on the Elements of Algebra - Σελίδα 128
των Bewick Bridge - 1821 - 227 σελίδες
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - 492 σελίδες
...ratio to B than E has to F. If therefore the firft of fix magnitudes has the fame ratio io the fecond, as the third to the fourth; and the third to the fourth has a greater ratio than the fifth to the fixth : then the firft to the fecond will have a greater...

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

Robert Simson - 1806 - 546 σελίδες
...separately, be proportionals, see N. they shall also be proportionals when taken joindy, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth....

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

John Playfair - 1806 - 320 σελίδες
...taken separately, be proportionals, they will also be proportionals when taken jointly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth....

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

John Mason Good - 1813 - 714 σελίδες
...taken separately, he proportionals, they shall also be proportionals, when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall he to the second, as the third and fourth together to the fourth....

An Easy Introduction to the Mathematics: In which the Theory and ..., Τόμος 2

Charles Butler - 1814 - 528 σελίδες
...both sides by bd, and (-—=—-, or) ~= 4-, that is,a:b::c:d. Euclid 17, 6. bd 61. If the first term be to the second, as the third to the fourth, and...as the fifth to the sixth, then will the first be to the second as the fifth to the sixth. Let a:b::c:d, and c : d : : e :f, then will a:b::e :f; for...

New Series of The Mathematical Repository, Τόμος 3

Thomas Leybourn - 1814 - 420 σελίδες
...found to be 3/. i8.r. g</, Required thejate per cent, per annum. a. If the first of six magnitudes be to the second as the third to the fourth, and the fifth to the second as the sixth to the fourth; Prove that the first and fifth together will be to...

Easy Introduction to Mathematics, Τόμος 1

Charles Butler - 1814 - 540 σελίδες
...or two more particulars will require an explanation. If four numbers are proportionals, that is, if the first be to the second as the third to the fourth, then will the first be to the third аз the second to the fourth; and this accounts for the usual...

An Elementary Treatise on Algebra

Bewick Bridge - 1818 - 254 σελίδες
...(dividing by cd) we have — = —,> or -=-1 5 .'. a : с : b : d, and b : d :; a.: c. cd cd, с а Тн. 5. "If there be six proportional quantities, and the...the fifth to the sixth ; then will the first " be to the second as the fifth to the sixth." For let a : b :: с : d, ij г iл. ac , с eae . and с:...

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

John Playfair - 1819 - 350 σελίδες
...demonstrated, A : C : : B : D, and inversely (A. 5.) C : A : : D : B. Therefore, &c. q. ED PROP. C. THEOE. If the first be to the second as the third to the fourth ; and if the first be a multiple or a part of the second, ihe third is the same multiple or the same part...

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

John Playfair - 1819 - 354 σελίδες
...taken separately, be proportionals, they will also be proportionals -when taken jointly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth....




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