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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... "
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Pągina 460
per Sir John Leslie - 1809 - 493 pągines
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pągines
...geometrical magnitudes, and therefore it is necessary to substitute another, which is as follows: — Def. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatever of the first and third being taken,...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 pągines
...whatever of G, H: therefore (V. def. 5) as E : G : : F : H. Therefore, &c. Cor. Likewise, if the first have the same ratio to the second, which the third has to the fourth, then also any like multiples whatever of the first and third have the same ratio to the second and...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pągines
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED COB. Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples whatever of the first and third shall have the*same ratio to the second...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 pągines
...ratio to the second, than the fifth has to the sixth. PROPOSITION XIV. THEOR. — If the first has the same ratio to the second which the third has to the fourth; then, if the first be greater than the third, the second shall be greater than the fourth ; and if...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 166 pągines
...multiple, &c. QED Recite (a) definitions 1, 2, A of b 5 -B D-0 H4 Th. If the first of four magnitudes have the same ratio to the second which the third has to the fourth ; then any equimultiples of the antecedents shall have the same ratio as any equimultiples of the consequents....
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 168 pągines
...having some common property ^ can have a ratio to one another. 5. The first of four magnitudes has the same ratio to the second which the third has to the fourth, when equimultiples of the first and third, also of the second and fourth, being taken ; if the multiple...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pągines
...has a greater ratio to the second than the fifth has to the sixth. PROP. XIV. THEOR. If the first has the same ratio to the second which the third has to the fourth, then, if the first be greater than the third, the second shall be greater than the fourth, and if equal,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 334 pągines
...two numbers. Let A=mB, and B=nC ; then A=mnC. PROP. IV. THEOR. If the first 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 the first and third, and any whatever of the second and...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pągines
...of the second, and the other of the fourth. PROP. IV. THEOREM. 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, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Llibre 1

Euclides - 1853 - 334 pągines
...is no necessity for all four to be of the same kind. OBS. 3. When the first of four magnitudes has the same ratio to the second which the third has to the fourth, the third clearly has the same ratio to the fourth which the first has to the second. Such will appear...
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