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" When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals. "
The Elements of Mathematical Analysis, Abridged: For the Use of Students ... - Page 11
by Nicolas Vilant - 1798 - 170 pages
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...which it has to the second. 1 1 . When four magnitudes are continual proportionals, t\\e first is said to have to the fourth the triplicate ratio of that which it has lit'... second, a:id so cm, quadruplicate, Sec. increasing the denomination stilt by unity, in any...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...has to the second. , XI. S*6 N. When four magnitudes are continual proportionals, the first Is said to have to the fourth the triplicate ratio of that which it has to the second^ and so on, quadruplicate, &c. increasing the denomination still by unity, in any number of...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...which it has to the second. XI. When four magnitudes are continued proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c. increasing the denomination still by unity in any number of proportionals....
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...is EX to PL, and ;PL to KO : But if four magnitudes be continual proportionsis, the fir«t is said to have to the fourth the triplicate ratio of that which it ha« to the second : Therefore the »olid AB has tu the solid KO, the triplicate ratio of that which...
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An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - Algebra - 1826 - 430 pages
...which it has to the lecond. XI. When four magnitudes are continued proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c. increasing the denomination still by unity in any number of proportionals....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...it has to the second. XL See N. When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c. increasing the denomination still by unity, in any number of...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...proportional to the other two. (455) XI. When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c. increasing the denomination still by unity, in any number of...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...it has to the second. XL See N. When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...so is EX to PL, and PL to KO. But if four magnitudes be continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second : therefore the solid AB has to KO the triplicate ratio of that which AB has to EX. But as AB...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...which it has to the second. . XI. When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c. increasing the denomination still by unity, in any number of...
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