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" Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 2
by Euclides - 1821
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 493 pages
...B—A:B:: D—C:D. PROP. XI. THEOR. The terms of an analogy are proportional by conversion ; that is, the first is to the sum or difference of the first and second, as the third to the sum or difference of the third and fourth. Let A: B:: C: D, and suppose A^B; then A: A=fcB:...
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An Elementary Treatise on Algebra

Bewick Bridge - Algebra - 1818 - 227 pages
...consequently, by Art. 99, ab : b :: cd : d. и Тн. 7. " If four quantities he proportional, U\K first is to " the sum or difference of the first and second, as the third to " the sum or difference of the third and fourth." For by THEOR. 6. a+b : b : : cd : d, and alternately...
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A Treatise on the Elements of Algebra

Bewick Bridge - Algebra - 1821 - 288 pages
...<-— vdb ==—=--, consequently, by Art. 99, a + b : b : : c+_d : d. Тн. 7. "If four quantities be proportional, the first is to " the sum or difference of the first and second, as the third to " the sum or difference of the third and fourth." For by THEOR. 6, a+_l : b : : с d : d, and...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...preceding, and theor. 3. 15. 5, it follows, that, "if four magnitudes be proportional, " by converting, the first, is to the sum or difference of the first...the sum or difference of the third " and fourth." PROP. XIX. THEOR. If the wAoie (^U), be to the wiwle (CD), as apart (-AE) taken away, is to apart(CF)...
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The First Six Books with Notes

Euclid - 1822 - 179 pages
...difference between the third and fourth to the fourth. Cor. 2. Prop. 25. 18. By conversion, when we infer that if there be four magnitudes proportional, the...or difference of the first and second, as the third to the sum or difference of the third and fourth. Prop. 21 and 25 and Cor. 1. Prop. 25. 19. Ex sequali,...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 210 pages
...orders. THEOREM 42. 122. If four quantities, a, b, c, d, be proportionals, the first will be to the sum of the first and second as the third is to the sum of the third and fourth. For, since a, b, c, d, are proportionals, ad=be. To each side of this equation...
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A Treatise on Algebra

George Peacock - Algebra - 1830 - 732 pages
...magnitudes be proportionals, they shall be proportionals also convertendo, or the first shall be to the difference of the first and second as the third is to the difference of the third and fourth." Let a : b :: c : d, then also a : a — b :: c : c—d. VI* a...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 183 pages
...difference between the third and fourth to the fourth. Cor. 2. prop. 25. 18. Byconversion; when we infer that if there be four magnitudes proportional, the...or difference of the first and second, as the third to the sum or difference of the third and fourth. Prop. 21, and 25. and Cor. 1. prop. 25. 19. Ex asquali,...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 172 pages
...to the fourth, 117. ART. 174. In a series of four proportional right lines, the first is to the sum of the first and second as the third is to the sum of the third and fourth, ibid. ART. 175. In a series of four proportional right lines, the first is...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...the third, together with the fourth, is to the fourth. 24. By addition, when the first is to the sum of the first and second, as the third is to the sum of 'the third and fourth. second, is to the second, as the excess of the third above the fourth, is...
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