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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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...H— DEF C— H— ill PROP. A. THEOR. IF the first of four magnitudes has to the second the See N. same ratio which the third has to the fourth ; then, if the first be greater than the second, the third is also greater than the fourth; and, if equal, equal; if less, less. Take any equimultiples...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...D. Therefore wA>nB, and wE<nF ; wherefore A : B>E : Fa. Therefore, &c. QED PROP. XIV. THEOR. Bookv. IF the first have to the second the same ratio which the third has to the fourth, and if the first be greater than the third, the second will be greater than the fourth; if equal, equal;...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 518 pages
...FH — F. Wherefore, as E • is to F, so is G to Hb. But, when four magnitudes are proportionals, if the first be greater than the third, the second shall be c!4. 5. greater than the fourth; and if equal, equal; if less, lessc. Wherefore, if E be greater than...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...shall all the antecedents taken together he to all the consequents. Prop. XIII. Theor.If the 6rst has to the second the same ratio which the third has to the fourth, hut 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; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...magnitudes, &c. QED PROP. A. THEOR. Bonx V. IF the first of four magnitudes has to the second SeeN. the same ratio which the third has to the fourth ; then, if the first be greater than the second, the third is also greater than the fourth; and if equal, equal; if less, less. Take any equimultiples...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...smaller numbers ? OF PROPORTION ". 53. Four quantities are said to be proportionals, when the first has to the second the same ratio which the third has to the fourth ; that is, when the first is the same multiple, part, or parts of the second that the third is of the...
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814
...terms in the form of a fraction . therewhen four quantities are proportionals, that is, when the has to the second the same ratio which the third has to the ih, it follows, that the fraction constituted by the terms of first ratio, -will be equal to the fraction...
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A Philosophical and Mathematical Dictionary: Containing an ..., Volume 2

Charles Hutton - Astronomy - 1815 - 686 pages
...then delivers the propositions, which are the following: " Prop. 1. 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...magnitudes, &c. QED OF EUCLID. PROP. A. THEOR. 121 Boo* V. IF the first of four magnitudes has to the secon9 the same ratio which the third has to the fourth ; then, if the first be greater than the second, the third is also greater than the fourth ; and if equal, equal ; if less, leps. i Take any...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...Therefore mAy»B, and mE/f »F, wherefore, . A : B7E : F (def. 1. 5.). Therefore, &r, QED PROP. XIV. THEOR. If the first have to the second the same ratio which the third has to the fourth, and if the first be greater thkn the third, the second shall be greater than the fourth ; if equal,...
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