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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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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...Supplement to this book may be used instead of what remaini of the book itMlf. 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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...any number of magnitudes, which was here applied to two.' QED PROPOSITION II. THEOREM. If thefirst magnitude be the same multiple of the second that...the second that the sixth is of the fourth ; then shall the first together with the Jifth be the same multiple of the second, that the third together...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...and CD together of E and F together. Wherefore, If any number of magnitudes fyc. QED 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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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...its part, the same multiple shall all the first magnitudes be of all the other. PROP. 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 geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...demonstration holds in any number of magnitudes which was here applied to two.' QED PROPOSITION 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 first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...applied to two. QED * Archimedes de Sphsera et Cylíndro, Prop. 4. lib. 2. PROPOSITION II. — THEOREM. If the first magnitude be the same multiple of the second that the third is of the fourth, and thefijth the same multiple of the second that the sixth is of the fourth ; then shall the first together...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...c any equimultiples whatever E, F, and of G, H any equimultiples whatever M, N. • PEOP. V. THEOE. If the first magnitude be the same multiple of the second that a third magnitude of the same kind is of the fourth, the first being greater than the third, and the...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...of its part, the same multiple is all the first magnitudes of all the others. QED PROP. II. THEOREM. If the first magnitude be the same multiple of the...second that the sixth is of the fourth ; then the first together with the fifth is the same multiple of the second, that the third together with the...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...+ 6 + c + &c.) + (a + 6 + c + &c.) to n terms - » (a + i + c + &c.) PROPOSITION II. THEOREM.—If the first magnitude be the same multiple of the second...of the fourth, and the fifth the same multiple of tlie second that the sixth is of the fourth ; then shall the first, together with the fifth, be the...
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Manual of Euclid. Books IV. V. VI.

Euclid - 1859 - 136 pages
...equations together, we find 0 + 4 + C + &C. =m(z + y4z + &c.) QEU PROPOSITION II.— THEOREM. If the first be the same multiple of the second that the third is of the fourth, and thefißh the same multiple of the second that the sixth is of the fourth; then the first and ßflh...
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