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" If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. "
An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 66
by Charles Butler - 1814
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A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1841 - 260 pages
...: cd : c, .-. inversely a : a6 : : c : cd. TH. 8. " If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference." For by TH. 6^ — =— = — =- , and od — T— = — — ; invert the last...
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The elements of algebra

James Wood - Algebra - 1841 - 496 pages
...inversely, a : a - b :: с : с — d. 236. When four quantities are proportionals, the sum of the rst and second is to their difference, as the sum of the third and fourth is to their difference. By Art. 233, a + bc + d • , . a -b с- d and by Art. 234, — ~ — = - ;...
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A manual of arithmetic

George Hutton (arithmetic master, King's coll. sch.) - 1844 - 274 pages
...8:4, then 6 : 6-3 :: 8 : 8-4, or 6 : 3 :: 8 : 4; for 6—3=2. and 84-4 = 2. 8. If four quantities are proportionals, the sum of the first and second is...their difference, as the sum of the third and fourth is to their difference; thus, if 6 : 3 :: 8: 4, then 6+3 : 6-3 :: 8+4 : 8-4, or 9 : 3 :: 12 : 4, for...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...then, by division, 12—3:3:: 8—2 : 2. Hence, If four magnitudes, <Sfc. Cor. The sum of the fir?t and second is to their difference, as the sum of the third and fourth is to their difference. Since - - AB : B : : C— D : D; Then, (8. 3,) AB : CD : : B : D. And, (16....
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The elements of algebra

James Wood - Algebra - 1845 - 442 pages
...— b : a :: с — d : c; and inversely, a : a — b :: с : с — d. 247. When four quantities are proportionals, the sum of the first and second is...their difference, as the sum of the third and fourth is to their difference. If a : b :: с : d; then a + b : a — b :: с + d : с — d. a + Ъ с +...
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The first principles of algebra, for the use of the boys of the Royal ...

Admiralty - 1845 - 154 pages
...ac For = .'. -jl=-jl (Art. 17.) a—bc — d ''• ~b~'~~d~ Or, ab:b::cd:d 89. If 4 quantities are proportionals, the sum of the first and second, is...their difference, as the sum of the third and fourth, is to their difference. That is, if a : b : : c : d then will a-\-b : a — b :: c-\-d : c— d For...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 pages
...108. Prop. 7- When four quantities are proportional, they are also proportional by mixing; that is, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. •dn di. "+' c+^ j T KIT. •"-* c — ^ For Prop. 5th — =-— , and Prop....
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...similar triangles it may be proved that of any three of the consecutive circles, the sum of the radii of the first and second, is to their difference, as the sum of the radii of the second and third, is to their difference. HINTS, &c. TO THE THEOREMS. BOOK VI. 3. THIS...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...:: C + D : C — D: that is, if four numbers be proportional, the sum of the first and second terms is to their difference, as the sum of the third and fourth terms is to their difference. It is evident, that if B be greater than A, the analogy would become...
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An Elementary Treatise on Algebra: Theoretical and Practical ...

Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...— b :: c : c — d. or a : b — a :: c : d — c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference. Admitting that a : b :: c : d, we are to prove that a-\-b : a — b :: c-\-d...
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