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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 Contents of the Fifth and Sixth Books of Euclid - Σελίδα 35
των Euclid, Micaiah John Muller Hill - 1900 - 143 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 σελίδες
...exceed the other. V. 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...equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less...

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

Sir John Leslie - 1809 - 542 σελίδες
...According to Euclid, " 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...equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less...

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

Sir John Leslie - 1809 - 522 σελίδες
...According to Euclid, " 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...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...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813 - 714 σελίδες
...exceed the other; 5. The first of four magnitudes is enid to hav<? the same ratio to the second, which the third has to the fourth, when any equimultiples...equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less...

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

Euclides - 1816 - 588 σελίδες
...exceed the other. y. 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...equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less...

Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - 1817 - 456 σελίδες
...According to Euclid, " 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...equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less...

The First Six Books with Notes

Euclid - 1822 - 222 σελίδες
...defines them thus: The Jirst of four magnitudes is said to have the same ratio to the second, which the third has to the 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
...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 fourth, when any equimultiples...equimultiples whatsoever of the second and fourth : if the multiple of the first be less than that of the third, the multiple of the second is also less...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 542 σελίδες
...according to Euclid. 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...equimultiples whatsoever of the second and fourth, if the multiple of the first be less than that of the second, the multiple of the third is also less...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - 1824 - 550 σελίδες
...according to Euclid. 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...equimultiples whatsoever of the second and fourth, if the multiple of the first be less than that of the second, the multiple of the third is also less...




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