| Sir John Leslie - Geometry, Analytic - 1809 - 542 pages
...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 pages
...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 - Astronomy - 1822 - 516 pages
...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 - Arithmetic - 1822 - 354 pages
...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 pages
...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 - 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 Playfair - Geometry - 1829 - 210 pages
...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 pages
...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 - Euclid's Elements - 1833 - 216 pages
...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 - Euclid's Elements - 1836 - 172 pages
...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... | |
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