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Books Books 1 - 10 of 107 on The first of four magnitudes is said to have the same ratio to the second, which....  
" The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 105
by Euclides - 1816 - 528 pages
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Trigonometry - 1806 - 311 pages
...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...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 493 pages
...exactly resemble the changes usually effected in the reduction of equations. According to Euclid, " The first of four magnitudes is said to have the same...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1810 - 518 pages
...as 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...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1813
...of the second, and the other of the fourth. Prop. IV. Thecir. If the first of four magnitue!p| lias 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 equimultiples...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...the first, &c. QED A 33 CV C J> Boo' V. PROP. IV. THEOR. SeeN. 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 equimultiples...
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An easy introduction to the mathematics: in which the theory and ..., Volume 1

Mathematics - 1814
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Trigonometry - 1819 - 333 pages
...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...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1819
...to the fourth, and if any equimultiples whatever he taken of the first and third, and any whatever of the second and fourth ; if the multiple of the first be equal to the multiple of the second, the multiple of the third will be equal to the multiple of the....
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The First Six Books with Notes

Euclid - 1822 - 179 pages
...be defined, is still a subject of controversy among geometers. Euclid defines them thus: The Jirst of four magnitudes is said to have the same ratio...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,...
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Universal Technological Dictionary: Or, Familiar Explanations of ..., Volume 2

George Crabb - Industrial arts - 1823
...the ratio of 6 to 2 is the same as that of 15 to 5, which is expressed thus : as 6 : 2 : : 15 : 5. The first of four magnitudes is said to have the same...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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