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" If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth... "
The student's algebra - Page 13
by John Darby (teacher of mathematics.) - 1829
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...number of magnitudes, which was here applied "to two.' QED PROP. II. THEOR. . IF the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...of magnitudes, which * was liere appiieci to two.' QE D. PROP. II. THEOR. IF the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth; then shall the first...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...of magnitudes, which was ' here applied to two/ Q. Б. D. PROP. II. THEOR. If Iheßrst magnitude be the same multiple of the second that the third is of the fourth, and the ßfth the same multiple of the second that the sixth is of the fourth ; then shall Iheßrst...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...number of mag' nitudes, which was here applied to two.' QED PROP. II. THEOR. If the first magnitude be the same multiple of the second that the third is of the fourtht and thejjfth the same multiple of the second that the sixth is of the fourth; then shall the...
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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
...any other equimultiples of A', B', and C'. PROPOSITION II. THEOREM. (475) If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first...
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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
...magnitudes were greater than two. Therefore, if any number, &c. PROP. II. THEOR. IF the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...number of ' magnitudes which was here applied to two.' QED PROP. II. THEOR. D IF the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth; then shall the first...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...number of mag' nitudes, which was here applied to two.' QED PROP. II. THEOR. If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is ofthefowth; then shall the first together...
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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Mathematics - 1841 - 144 pages
...the third and sixth together, is of b the fourth. PROP. III. THEO. If the first of four magnitudes be the same multiple of the second that the third is of the fourth, and if any equimultiples whatever of the first and third be taken, those shall be equimultiples ; one...
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Lectures on the Principles of Demonstrative Mathematics

Philip Kelland - Algebra - 1843 - 168 pages
...important propositions are omitted in the Fifth Element ; such as " four magnitudes are proportional when the first is the same multiple of the second that the third is of the fourth."* Truths of this kind are clear by their own light from the arithmetical notion of proportion, but are...
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