 | Robert Simson - 1806 - 518 σελίδες
...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... | |
 | 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... | |
 | John Leslie - 1809 - 542 σελίδες
...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... | |
 | Euclid - 1810 - 518 σελίδες
...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... | |
 | John Mason Good - 1813 - 722 σελίδες
...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... | |
 | 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... | |
 | Euclides - 1814 - 558 σελίδες
...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... | |
 | Euclides - 1816 - 528 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... | |
 | Sir John Leslie - 1817 - 454 σελίδες
...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... | |
 | Euclid, John Playfair - 1819 - 348 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... | |
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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... 
