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" Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio. "
The Operative Mechanic, and British Machinist: Being a Practical Display of ... - Page 674
by John Nicholson - 1825 - 795 pages
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Elements of Geometry: With Their Application to the Mensuration of ...

Thomas Simpson - Geometry - 1760 - 296 pages
...proporE. tional (or in continual proportion) when the firft i. 2. 4. . js to ^ feconj) as ,-he fecond to the third, as the third to the fourth, as the fourth to the fifth, and fo on. 7. In a feries, or rank of quantities continually proportional, the ratio of the firft and third,...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - Mathematics - 1812 - 620 pages
...Proportional, OF in Continued Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to...the fourth, as the fourth to the fifth, and so on, all in the same common ratio. As in the quantities 1, 2, 4, 8, 16, &c ; where the common ratio is equal...
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The Elements of Algebra: Designed for the Use of Students in the University

James Wood - Algebra - 1815 - 338 pages
...PROGRESSION. (214.) Quantities are said to be in geometrical progression, or continual proportion, when the first is to the second, as the second to the third, ajid as the third to the fourth, &c. that is, when every succeeding term is a certain multiple, or...
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A Course of Mathematics: In Two Volumes. For the Use of Academies ..., Volume 1

Charles Hutton - Arithmetic - 1818 - 646 pages
...Proportional, or in Continued Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to...third, as the third to the fourth, as the fourth to the Mb, and so on, all in the same common ratio. As in the quantities J, 2, 4, 8, 16, &c. ; where the common...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 10

William Nicholson - Natural history - 1821 - 376 pages
...PROGRESSION, geometrical. Quantities are said to be in geometrical progression, or continual proportion, when the first is to the second, as the second to the third, and as the third to the fourth, &c. that is, when every succeeding term is a certain multiple, or part...
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Elements of Science and Art: Being a Familiar Introduction to ..., Volume 2

John Imison - Art - 1822 - 488 pages
...: 1 : : 12:4; then by division 3 — 1 : 1 : : 12 — 4 : 4 and 3 — 1 : 3 : : 12 — 4> : 12. 63. Continued proportion is when the first is to the second...the fourth ; as the fourth to the fifth ; and so on. 64. Compound ratio is formed by the multiplication of several antecedents and the several consequents...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 pages
...Proportional, or in Continued Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to...the fourth, as the fourth to the fifth, and so on, all in the same common ratio. As in the quantities 1, 2, 4, 8, 16, &c. ; where the common ratio is...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...in order. 12. Magnitudes, are said to be continually proportional, when the first has the same ratio to the second, as the second to the third, as the third to the fourth, and so on13. The ratio of the first, of any number of magnitudes of the same kind, to the last, is...
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The Builder's Practical Guide: Containing a Complete Explanation of the ...

John Nicholson (Civil engineer) - Building - 1830 - 240 pages
...antecedent. Thus, if 3 : 1 :: 12 : 4 ; then, by division, 3 — 1 : 1 :: 12 — 4 : 4, and 3—1 : 3:: 12— 4: 12. 98. Continued proportion is when...ratios together, in the following manner : If A be to B as 3 to 5, B to C as 5 to 8, and C to D as 8 to 6 ; then A will be D, as ==^ , that is> A : D...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...B. [П. } l 11. Any number of magnitudes of the saine kind are said to be in continued proportion, when the first is to the second, as the second to the third, as the third to the fourth, and so on. Magnitudes A, B, C, D, Sec. which are in continued proportion, may be thus written, A :...
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