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" 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 plane geometry; or, The first six books of Euclid, ed. by W ... - Strona 67
autor: Euclides - 1863
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - Liczba stron: 518
...mutual relation of two magnitudes of the same kind Ste N ' to one another, in respect of quantity.' IV. Magnitudes are said to have a ratio to one another,...whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - Liczba stron: 311
...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 ...

Sir John Leslie - 1809 - Liczba stron: 524
...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...whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - Liczba stron: 518
...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 ..., Tom 5

John Mason Good - 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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Easy Introduction to Mathematics, Tom 1

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

Euclides - 1816 - Liczba stron: 528
...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...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - 1817 - Liczba stron: 432
...resemble exactly the changes usually effected in the reduction of equations. According to Euclid, " The first of four magnitudes is said to have the same...whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - Liczba stron: 333
...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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