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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. "
A Course of Mathematics: Composed for the Use of the Royal Military Academy - Page 332
by Charles Hutton - 1860 - 895 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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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 - Mathematics - 1816 - 610 pages
...Third Proportional to the first and second. 81. Of four proportional quantities, the last is s.iid to be a Fourth Proportional to the other three, taken...common ratio. As in the quantities 1, 2, 4, 8, 16, Sec ; where the common ratio is equal to 2. 83. Of any number of quantities, A, a, c, D, the ratio...
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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 between the other two ; and the last, a Third Proportional to the first and second. 81. Of four proportional quantities, the last is said 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
...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 as the second to the...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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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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A Course of Mathematics for the Use of Academies: As Well as ..., Volume 1

Charles Hutton - Mathematics - 1825 - 608 pages
...a Third Proportional to the first and second. 81. Of four proportional quantities, the last is raid to be a Fourth Proportional to the other three, taken...in the same common ratio. As in the quantities 1, '-, 4, 8, 16, fee , where the common ratio is equal to 2. 83. Of any number of quantities, A, B, c,...
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The Operative Mechanic, and British Machinist: Being a Practical ..., Volume 1

John Nicholson - Machinery - 1825 - 838 pages
...by division, 3 — I : 1 :: 12— 4 : 4, and 3—1 : 3 :: 12—4 : 12. 98. Continued proportion is when the first is to the second as the second to the...the fourth ; as the fourth to the fifth ; and so on. 99. Compound ratio is formed by the multiplication of several antecedents and the several consequents...
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The Operative Mechanic, and British Machinist: Being a Practical Display of ...

John Nicholson (civil engineer.) - Great Britain - 1825 - 1008 pages
...then, by division, 3 — 1 : 1 :: 124 : 4, and 3—1 : 3 :: 12—4 : 12. 98. Continued proportion is when the first is to the second as the second to the...third ; as the third to the fourth ; as the fourth to dx fifth ; and so on. 99. Compound ratio is formed by the multiplication of several antecedents and...
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