 | Sir John Leslie - 1809 - 542 σελίδες
...alternation and inversion, A=fcE : B : : C=J=F : D. PROP. XX. THEOR. In continued proportionals, the difference between the first and second is to the second, as the difference between the first and last terms to the sum of all the terms, excepting the first. Let A:B::B:C::C:D::D:E; then... | |
 | Euclides - 1821 - 294 σελίδες
...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 the...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 - 1822 - 516 σελίδες
...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 the...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 - 1822 - 354 σελίδες
...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 the...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 - 222 σελίδες
...fourth. Cor. Prop. 21. 17- By division, when we infer that if there be four magnitudes proportional, the difference between the first and second is to the...second as the 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... | |
 | Rev. John Allen - 1822 - 508 σελίδες
...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 Playfair - 1829 - 210 σελίδες
...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 the...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... | |
 | John Darby (teacher of mathematics.) - 1829 - 212 σελίδες
...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 the...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... | |
 | Euclid - 1833 - 216 σελίδες
...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 the...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 - 1836 - 172 σελίδες
...ART. is called COMPONENDO, or Composition. ART. 173. In a series of four proportional right lines, the difference between the first and second is to the...difference between the third and fourth is to the fourth. Let AB be to CD as EF to GH. Then the difference between AB and CD is to CD as the difference between... | |
| |
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... 
