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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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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...equal to these others, or equimultiples of them. Prop. A. Theor. If the first of four macnltudei has to the second the same ratio which the third has to the fourth; then, if the fine be greater than the second, the third is als» greater than the fointh; and, if equal, equal ;...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...; therefore (def 5. 5.) A : B : : A+C+E : B+D+F. Therefore, &c, QED PROP. XIII. THEOR. If thejlrst have to the second the same ratio which the third has to tht fourth, but the third to the fourth a greater ratio than the fifth has to the sixth ; the first...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...number of magnitudes. Therefore, if there be any number, &c. QED PROP. XXIV. THEOR. 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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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Geometry - 1821 - 898 pages
...three of which are in arithmetic and the last three in harmonic progression ; prove that the first has to the second the same ratio which the third has to the fourth. ч 18. The sum of three terms of an harmonic progression, whose first term is -, is = — ; determine...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...E : H. In like manner we may proceed for any number ot magnitudes. QED PROP. XXIV. If the first has to the second the same ratio which the third has to the fourth ; and the fifth to the se••ond the same ratio which the sixth has to the fourth ; the first and...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...H. In like manner we may proceed for any number of magnitudes. QED tt PROP. xxiv. I/ the first has to the second the same ratio which the third has to the fouttY\ -, *a& v\» fe.Wtv \x> V^^ wtcond the same ratio vrtucVi V\ia %vs.\Xx \\a& \» fourth; the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...equimultiples of A, C, E, and L, •I, N equimultiples of B, D, F; if PROP. XIII. THEOR. If the ßrst 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 ßrst shall also...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...the second a less ratio than the third has to the fourth." "Prop. i. If the first of four magnitudes have to the second the same ratio which the third has to the fourth; then, if the first be equal to the second, the third is equal to the fourth; if greater, greater; if less, less." Dr. Robertson...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...then delivers the propositions, which are the following : "Prop. i. If the first of four magnitudes have to the second the same ratio which the third has to the fourth ; then, if the first be equal to the second, the third is equal to the fourth ; if greater, greater ; if less, less." " Prop....
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An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - Algebra - 1826 - 430 pages
...: nA : : rB : nB. PROF. A. THEOR. If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then if the first be greater than the second, the third is also greater than the fourth ; if equal, equal ; and if less, less. DEMONSTRATION....
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