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" THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 79
by Dennis M'Curdy - 1846 - 138 pages
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...= C6:D3 B 6 : E 4 = F9:C6 E4 : G2 = H18:F9 H 12: G2 = H18:D3 PROF. XXIV.— THKOn. If the first has to the second the same ratio which the third has to the fourth; and thefiflh to the second the same ratio which the sixth has to the fourth ; the first and fiflh 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
...r's, and <?'s on the right ; a _р and therefore a : n :: p : z. PROPOSITION XXIV. If the first has to the second the same ratio which the third has to the fourth, and the fifth to the second the same ratio which the sixth has to the fourth ; the first and fifth...
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Problems and Examples

Harvey Goodwin - 1862 - 174 pages
...arithmetical, and the last three in harmonieal progression ; it is required to" prove that the first has to the second the same ratio which the third has to the fourth. 10. If P, Q, R be respectively the^th, 2th, and rih terms of an harmonieal series, prove that (p -q)PQ...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...together. (v. def. 5.) Wherefore, if any number, &c. QED PROPOSITION XIII. THEOREM. ]f the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
.... . V. 22. 8. 'Ex aquali in proportione perturbata,' or, 'Ex asquo perturbato ' ........ V. 23. 9. If the first have to the second the same ratio which the third has to the fourth ; and the fifth to the second, the same ratio which the sixth has to the fourth ; the first and fifth...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...together. (v. def. 5.) Wherefore, if any number, &c. QED PROPOSITION Xin. THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also...
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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
...the number of magnitudes. Wherefore, if there be any number &c. QED II PROPOSITION 24. THEOREM. Tf the first have to the second the same ratio which the third has to the fourth, and the fifth have to the second the same ratio which the sixth has to the fourth, then the first and...
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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
...be the number of magnitudes. Wherefore, if there be any number &c. QBD H PROPOSITION 24. THEOREM. Tf the first have to the second the same ratio which the third has to the fourth, and the fifth have to the second the same ratio which the sixth has to the fourth, then the first and...
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Manual of Euclid: Books IV, V, VI.

Euclid - 1868 - 138 pages
...кai irpurov irpbç ¡fvrepov fieíZova \oyov é'lie ijirep irifiirTov irpoç êKTOV. If the first has to the second the same ratio which the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the sixth; the first has also to...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...magnitudes. Therefore, if there be any number, &c. QED PROPOSITION XXIV. THEOREM. If the first has to the second the same ratio which the third has to the fourth ; and the fifth to the second the same ratio which the sixth has to the fourth; the first and fifth...
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