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A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Side 198
av Euclides - 1864
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 sider
...of a lefs, when the greater is meafured by the lefs, that is, ' when the greater con' tains the lefs a certain number of times exactly.' III. " Ratio is a mutual relation of two magnitudes of the fame kind to see N. " one another, in refpect of quantity." IV. Magnitudes are faid to have a ratio...
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The Mathematical Correspondent: Containing, New Elucidations ..., Volum 1

George Baron - 1804
...by seven dots placed in the annexed straight line A. § 2. A greater number is a multiple of a less, when the greater contains the less a certain number of * times exactly. Thus the number 12 repre- B .... | .... | .... sented by B is a multi- C . . . . pie of 4 represented...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 sider
...times, exactly, in the greater. II. A greater magnitude is said to be a multiple of a less, when die greater is measured by the less, that is, when the...same kind, to one another, in respect of quantity. Hook V. Magnitudes are said to be of the same kind, when the less can be multiplied so as to exceed...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 sider
...contained a certain number of times exactly in the greater,' II. A greater magnitude is said to be a multiple of a less, when the greater is measured...contains the less a certain number of times exactly.' HI. ' Ratio is a mutual relation of two magnitudes of the same kind Ste N ' to one another, in respect...
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volum 1

Isaac Dalby - 1807
...DEFINITIONS. 65. THE following Definition of Ratio it usually given in the 5th. Book of Euclid's Elements. " Ratio is a mutual relation of two -magnitudes of the...same kind to one another in respect of quantity." This definition is frequently objected to as imperfect and obscure. And it seems difficult to acquire...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 493 sider
...author of the Elements has likewise given what Dr Barrow calls a metaphysical definition of ratio : " Ratio is a mutual relation of two magnitudes of the...same kind to one another, in respect of quantity" This sentence, as it now stands, appears either tautological, or altogether devoid of meaning ; and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 sider
...contained a certain number of times exactly in the greater.' II. A greater magnitude is said to be a multiple of a less, when the greater is measured...the less a certain number of times exactly.' III. 1 Ratio is a mutual relation of two magnitudes of the same kind See Nbte. ' to one another, in respect...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1813
...a, certain number of tiuies exactly in the greater. 2. Л greater magnitude is said to be a muftipfe of a less, when the greater is measured by the less,...that is, when the greater contains the less a certain rtu «her of times exactly. 3. flatio is a mutual relation of two magnitudes of the same kind to one...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...contained a certain number of times exactly ' in the greater." II. A greater magnitude is said to be a multiple of a less, when the greater is measured...is a mutual relation of two magnitudes of the same See N. ' kind to one another, in respect of quantity.' IV. Magnitudes are said to have a ratio to one...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...contained a certain number of times exactly ' in the greater.' II. A greater magnitude is said to be a multiple of a less, when the greater is measured...the less a certain number of times ' exactly.' III. c Ratio is a mutual relation of two magnitudes of the same See N. ' kind to one another, in respect...
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