 | 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... | |
 | Rev. John Allen - Astronomy - 1822 - 518 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... | |
 | 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... | |
 | Euclid - 1822 - 216 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... | |
 | 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,... | |
 | 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... | |
 | 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... | |
 | Euclid - Euclid's Elements - 1833 - 214 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... | |
 | 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... | |
 | 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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