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" The difference between the first and second terms of a proportion is to the second, as the difference between the third and fourth is to the fourth. The given proportion, a : b : : c : d, , ... ac may be written, 6~d... "
First Lessons in Algebra: In which the Elements of the Science are ... - Page 122
by Samuel Alsop - 1856 - 135 pages
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pages
...Prop. 21. Book 5. 1 7- Dividendo ; when it is concluded, that if there be four magnitudes proportional, the difference between the first and second is to...difference between the third and fourth is to the fourth. Note. If A : B : : C : D then A— B : B : : C— D : D. This def. is proved by Cor. 2. Prop. 25. Book...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...Prop. 18th of this book. 19. Dividing ; when it is inferred, if four magnitudes be pro portional, that the difference between the first and second is to...difference between the third and fourth is to the fourth. Prop. 17th of this book and scholium thereto. 20. Con-verting; when it is inferred, if four magnitudes...
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The Complete Practical Arithmetician: Containing Several New and Useful ...

Thomas Keith - Arithmetic - 1822 - 354 pages
...or A+BXD=C+DXB, there fore (art. 12.) A+B : B :: C-{-D : D. 16. If four quantities be proportional, the difference between the first and second, is to...difference between the third and fourth, is to the fourth. Thus, if A : B :: c : D, then DIVIDENDO, A — B : B :: c — D : D. For AD=BC (art 11.) take DB from...
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The First Six Books with Notes

Euclid - 1822 - 222 pages
...excess above the fourth. Cor. 2. If there be four magnitudes proportional, AF,g, 34. to B as C to D ; the difference between the first and second is to...second, as the difference between the third and fourth to the fourth. For, since A is to B as C to D, B is to A as D to C (1), therefore B is to the difference...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 508 pages
...magnitudes be proportional; the difference between the first and second, is to the second or first, as the difference between the third and fourth, is to the fourth or third, as the case may be. four proportionals, the antecedents A —— I g Part I .—Let AB, CD,...
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The student's algebra

John Darby (teacher of mathematics.) - 1829 - 212 pages
...to the fourth. Thus, if a;b; ;c'd, then will a+b:by.c+d;d. 4. If four quantities be proportionals, the difference between the first and second is to...difference between the third and fourth is to the fourth. Thus,ifa:6::e;rf; then will a— b ; b : ; c — did. 5. If four quantities be proportionals, the sum...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...+ D B D' BD ' ' ' ^S~ " " D •> or A + B : B : : C + D : D. 38. ^ four quantities be proportional, the difference between the first and second is to...difference between the third and fourth is to the fourth. A - BAr BB: • ''c For -=£, and2_- D- . B !>' B-JJ' A — B : B : : C — D : D. 39. If four quantities...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 216 pages
...excess above the fourth. Fig. 24. Cor. 2. If there be four magnitudes proportional, A to B as C to D, the difference between the first and second is to...second, as the difference between the third and fourth to the fourth. (i )Prop.20. For, since A is to B as C to D, B is to A as D to C (1), therefore B is...
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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
...In a series of four proportional right lines, the difference between the first and second is to tho second as the difference between the third and fourth is to the fourth, 117. ART. 174. In a series of four proportional right lines, the first is to the sum of the first and...
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The first principles of algebra, for the use of the boys of the Royal ...

Admiralty - 1845 - 152 pages
....'. -£- + !=— +1 (Art. 16.) a+b c+d Or, a+b : b :: c+d: d 88. If 4 quantities are proportionals, the difference between the first and second, is to...second, as the difference between the third and fourth, iğ to the fourth. That is, if a : b : : c : d then will a — Ь:Ь:: c—d : d _ ac For = .'. -jl=-jl...
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