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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 ; then shall... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Side 71
av Dennis M'Curdy - 1846 - 138 sider
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 sider
...Book V. « holds in any number of magnitudes, which was here applied "to two.' QED PROP. II. THEOR. . IF the first magnitude be the same multiple of the...the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second, that the third together...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...was here applied to two.' QED PROP. II. THEOR. IF the first magnitude be the same multiple of tlie second that the third is of the fourth, and the fifth...of the second that the sixth is of the fourth; then shall the first together with the fifth be the same multiple of the second, that the third together...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...demonstration holds in any number of magnitudes, which * was liere appiieci to two.' QE D. PROP. II. THEOR. IF the first magnitude be the same multiple of the...of the second that the sixth is of the fourth; then shall the first together with the fifth be the same multiple of the second, that the third together...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1819
...be of all the other. Prop. II. Theor. If the first magnitude be the sume multiple of the second thai the third is of the fourth, and the fifth the same multiple of the second thiit the sixth is of tin' fourth ; then shall the first together with (he fifth be the »ame multiple...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 sider
...demonstration * holds in any number of magnitudes, which was here applied * to two.' Q- ED PROP. II. THEOR. IF the first magnitude be the same multiple 'of the...the same multiple of the second that the sixth is ofthe fourth; then shall the first together with the fifth be the same multiple of the second, that...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...any ' number 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 together...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...demonstration holds in any 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 - 1828 - 324 sider
...and C were supposed to be any other equimultiples of A', B', and C'. PROPOSITION II. THEOREM. (475) If the first magnitude be the same multiple of the...the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second, that the third together...
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The student's algebra

John Darby (teacher of mathematics.) - 1829
...which may be found in the fifth book of Euclid. 1. Four quantities are proportionals, when the first is the same multiple of the second, that the third is, of the fourth. Thus, if a, b, c, and d, be the four proportionals, they are placed thus, a ; b ; ;c ; d, and ac are...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...number of magnitudes, which was here ' applied to two.' QED ^^ PROPOSITION II. THHOR. — If the Jirst magnitude be the same multiple of the second that...the second that the sixth is of the fourth ; then shall theJirst together with the fifth be the same multiple of the second, that the third together...
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