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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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...holds in any number of magnitudes, which was here applied to two.' QED PROPOSITION II. THEOREM. Jf the first magnitude be the same multiple of the second...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 Notes

Eucleides - 1860 - 396 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...of the fourth, and the fifth the same multiple of thesecond that the sixth is of the fourth. CONSEQUENCES. ^ The third is the same multiple or submultiple...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...and у A = m E, B = n E, and C = p E ; .-. m E + n E + p E = (m + и + p) E. Pnоr. II. — TUEOK. If the first magnitude be the same multiple of the second that the third is of the fourth, and thefifth-thc same multiрle of the second that the sixth is of the fourth ; then shall the first. together...
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The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...then a + e + ff + k is the same multiple of b that с +f+ h + /is of d. PROPOSITION III. 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 any equimultiples ; these shall be equimultiples, the one...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...demonstration holds in any number of magnitudes, which was here applied to two.' QED PROPOSITION II. THEOREM. If the first magnitude be the same multiple of the second that the third is of the fourth, and the liflh the same multiple of the second that the sixth is of the fourth; then shall the jirst together...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...them is of its part, the same multiple shall all the first magnitudes be of all the others ? Prop. 2. 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...demonstration holds in any number of magnitudes, which was here applied to two.' QED PROPOSITION II. 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 for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...that the whole of the last, namely. DL, is of/7. H J K HC JL F PROPOSITION 3. THEOREM. 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 equimtiltiples, the one...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...of C, that the whole of the last, namelv, H DL,isofF, G H J K PROPOSITION 3. THEOREM. 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...demonstration holds m any number of magnitudes, which was here applied to two.' QED PROPOSITION II. THEOREM. Jf the first magnitude be the same multiple of the second...of the second that the sixth is of the fourth; then shall Hie first together with the fifth be the same multiple of the second, that the third together...
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