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Bøker Bok 110 av 21The difference between the first and second terms of a proportion is to the second,...
" 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... "
A Treatise on Arithmetic: Through which the Entire Science Can be Most ... - Side 287
av Noble Heath - 1856 - 455 sider
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 493 sider
...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...
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The Elements of geometry [Euclid book 1-3] in general terms, with ..., Del 3

Euclides - 1821
...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...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 494 sider
...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...
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The Complete Practical Arithmetician: Containing Several New and Useful ...

Thomas Keith - 1822 - 332 sider
...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...
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The First Six Books with Notes

Euclid - 1822 - 179 sider
...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...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 494 sider
...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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Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - 186 sider
...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...
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The student's algebra

John Darby (teacher of mathematics.) - 1829
...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...
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The first six books of the Elements of Euclid: with notes

Euclid, Thomas Elrington - 1833 - 183 sider
...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...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 sider
...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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