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" If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth... "
Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...
των John Mason Good - 1813
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 σελίδες
...hypothesis A=mB, therefore A=mnC. Therefore, &c. QED PROP. IV. THEOR. IF the first of four magnitudes have the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be taken of the first and third, and any whatever of the second and...

Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 522 σελίδες
...in the reduction of equations. According to Euclid, " The first of four magnitudes is said to have the same ratio to the second which the third has to...being taken, and any equimultiples whatsoever of the aecmxd and fourth ; if the multiple of the first be less than that of the second, the multiple of the...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 554 σελίδες
...therefore E is to G, so isc F to H. Therefore, if the first, &c. QED C0R. Likewise, if the first have the same ratio to the second, which the third has to the fourth, then also any equimultiple!; 1 3. 5. b Hypoth. KEA GM L' FCDHN whatever of the first and third have...

Easy Introduction to Mathematics, Τόμος 1

Charles Butler - 1814 - 540 σελίδες
...comparison of one number to another is called their ratio ; and when of four giren numbers the first has the same ratio to the second which the third has to the fourth, these four numbers are said to be proportionals. Hence it appears, that ratio is the comparison of...

A Philosophical and Mathematical Dictionary: Containing an ..., Τόμος 2

Charles Hutton - 1815 - 686 σελίδες
...of the third is also equal to that of the fourth ; or if when the multiple of the first is greater than that of the second, the multiple of the third is also greater than that of the fourth : then, the first X)f the four magnitudes shall be to the second as...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 σελίδες
...fourth D. 1f, therefore, the first, &c. QED A CD 2.5. BouK V. See N. If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultir...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 350 σελίδες
...A = mB, therefore A~mn C. Therefore, &c. Q, ED PROP. IV. THEOR. If thefirst of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be taken of thefirst and third, and any whatever of the second and...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 514 σελίδες
...third is also equal to that of the fourth; or, if the multiple of the * SBP note. first be greater than that of the second, the multiple of the third is also greater than that of the fourth. VL Magnitudes which haye the same ratio are called proportionals....

The First Six Books with Notes

Euclid - 1822 - 222 σελίδες
...controversy among geometers. Euclid defines them thus: The Jirst of four magnitudes is said to have the same ratio to the second, which the third has...fourth, when any equi-multiples whatsoever of the Jirst and third being taken, and any equi-multiples whatsoever of the second and fourth being taken,...

Universal Technological Dictionary: Or, Familiar Explanations of ..., Τόμος 2

George Crabb - 1823 - 704 σελίδες
...15 to 5, which is expressed thus : as 6 : 2 : : 15 : 5. The first of four magnitudes is said to have the same ratio to the second which the third has to...the multiple of the first be less than that of the third, the multiple of the second is also less than that of the fourth ;• if equal, equal ; and if...




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