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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 school edition. Euclid's Elements of geometry, the first six books, by R ... - Σελίδα 238
των Euclides - 1864
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Euclid, book v. proved algebraically, so far as it relates to commensurable ...

Charles Lutwidge Dodgson - 1874 - 96 σελίδες
...The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when the first is the same multiple, part, or fraction of the second which the third is of the fourth...

Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - 1874 - 80 σελίδες
...by this Definition, to exclude infinite magnitudes. 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 whatsoever of the first and third being taken, and any equimultiples whatsoever...

The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 σελίδες
...the less can be multiplied so as to exceed the other. 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 whatsoever of the first and third being taken, and any equimultiples whatsoever...

Euclidian Geometry

Francis Cuthbertson - 1874 - 400 σελίδες
...(v. 3) Euclid's test of proportion is the following : 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 whatever of the first and third being taken and any equimultiples whatever of...

The Elements of Euclid, with Many Additional Propositions and Explanatory ...

Euclid - 1876 - 240 σελίδες
...» . B = n . m . b that is, n . A, n . B are equimultiples of a and b. PROPOSITION IV. THEOREM. — If the first of four magnitudes has the same ratio...ratio to any equimultiples of the second and fourth, i. «. " the equimultiple of the first shall have the same ratio to that of the second which the equimultiple...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 446 σελίδες
...greater ratio to the second, than the fifth has to the sixth. PROPOSITION XIv. THEOREM; Jf the first has the same ratio to the second which the third has to the fourth i then, if thefrst be greater than the third, the second shall be greater than the fourth ; and if...

Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 452 σελίδες
...into three, and also into five equal parts. 6. When is the first of four magnitudes said to have the the same ratio to the second which the third has to the fourth ? Prove that triangles which have the same altitude are to one another as their bases. Show also that...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 426 σελίδες
...DEF. Euclid's test of a proportion is as follows : — "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 plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 σελίδες
...another, in respect of quantity, is called their ratio. XXX. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fouitl', when any equimultiples whatsoever of the first and third i being taken, ai;d any equimultiples...

First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879 - 414 σελίδες
...figures. 2. About a given circle describe a triangle equiangular to a given triangle. 3. If the first have the same ratio to the second which the third has to the fourth, but the third to the fourth a greater ratio than the fifth to the sixth, the first shall have to the...




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