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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 ... - Page 71
by Dennis M'Curdy - 1846 - 138 pages
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Manual of Euclid: Books IV, V, VI.

Euclid - 1868 - 138 pages
...equations together, we find a + 6 + c + &c. = m(œ+y+zt- &c.) QED PROPOSITION II.— THEOREM. If the first be the same multiple of the second that the third...the second that the sixth is of the fourth; then the first and fifth together shall be the same multiple of the second, that the third and sixth are of...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...omitted, and the numerator is said to be the ratio. Corollary 2. — If the first of four magnitudes be the same multiple of the second that the third is of the fourth, the ratio of the first magnitude to the second will be the same as the ratio of the third magnitude...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...the same multiple of B, that C, F together is of D. QED PROPOSITION III. (Eucl. v. 3.) If the first be the same multiple of the second that the third is of the fourth ; and if of the first and third there be taken equimultiples, these must be equimultiples, the one of the...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...demonstration holds in any number of magnitudes, which was here applied to two." QED PROPOSITION 2. —Theorem. 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 tIie tiiird together...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...demonstration holds in any number of magnitudes, which was here applied to two.' QEn PROPOSITION IL THEOREM. 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, with Many Additional Propositions and Explanatory ...

Euclid - 1876 - 240 pages
...second which the third is of the fourth, and if of the first and third there be taken equimultiples. If the first magnitude be the same multiple of the...multiple of the second that the sixth is of the fourth. CONSEf/UENCES. I The third is the same multiple f or submultiple of thefourth. These shall be equimultiples,...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin SMITH - 1876 - 382 pages
...A, B together is the same multiple of C, D together that PROPOSITION II. (Eucl. v. 2.) If (he first be the same multiple of the second that the third...multiple of the second that the sixth is of the fourth ; the first together with the fifth must be the same multiple of the second, that the third together...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...Of d PROPOSITION II. (Eucl. v. 2.) If Oie first be the same multiple of the second that the third it of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; the first together with the fifth must be the same multiple of the second, that the third together...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides - 1878 - 398 pages
...together is the same multiple of C, D together that PROPOSITION II. (Eucl. T. 2.) If the first lie the same multiple of the second that the third is...multiple of the second that the sixth is of the fourth ; the first together with the fifth must be the same multiple of the second, that the third together...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879 - 414 pages
...figures. 2. About a given circle describe a triangle equiangular to a given triangle. 3. If the first be the same multiple of the second that the third is of the fourth, and if of the first and the third there be taken equimultiples, these shall be equimultiples, the one of...
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