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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... "
An Elementary Treatise on Algebra: Theoretical and Practical ... - Σελίδα 331
των James Ryan - 1826 - 383 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 σελίδες
...IV. THEO R. '"fee N.' JF the firft of four magnitudes has the fame ratio to the '•• ''. fecond which the third has to the fourth; then any equimultiples whatever of the firft and third fhall have the fame ratio to any equimultiples of the fecond and fourth, viz. ' the...

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 σελίδες
...Book V. SccN. I PRO P. IV. THEO R. F the firft of four magnitudes has the fame ratio to _ the fecond which the third has to the fourth ; then any equimultiples whatever of the firft and third fhall » have the fame ratio to any equimultiples of the fecond and fourth, viz. «...

The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 σελίδες
...Hypoth. c 3. def. PRO P. IV. THEO R. IF the firft of four magnitudes has the fame ratio td the fecond which the third has to the fourth ; then any equimultiples whatever of the firft and third mail have the fame ratio to any equimultiples of the fecond and fourth, viz. * the...

The Elements of Mathematical Analysis, Abridged: For the Use of Students ...

Nicolas Vilant - 1798 - 170 σελίδες
...m В==я пг X Bi PROPOSITION IV.— THEOREM; if the firft of four magnitudes have the fame ratio which the third has to the fourth ; then any equimultiples whatever of the firft and third mall have the fame ratio to any equimultiples of the fécond and fourth* viz. the equimultiple...

The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...C^ED Kr EABGC I D PROP. IV. THE OR. IF the firft of four magnitudes has the fame ratio to the fecond which the third has to the fourth; then any equimultiples whatever of the firft and third fhall have the fame ratio to any equimultiples of the fecond and fourth, viz. * the...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 σελίδες
...sixth, is of the fourth D. If, therefore, the first, &c. QED K H EABGCD BookV. PROP. IV. THEOR. See N. IF the first of four magnitudes has the same ratio to the second which the third hath to the fourth, then any equimultiples whatever of the first and third shall have the same ratio...

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

John Playfair - 1806 - 311 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 - 493 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 the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever...

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

Euclid - 1810 - 518 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 the'...

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

John Mason Good - 1813
...less can be multiplied so as to 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 whatsoever of the first and third being taken, and any equimultiples whatsoever...




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