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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  "
Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ... - Σελίδα 102
των Euclid - 1845 - 199 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 488 σελίδες
...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...

The Mathematical Correspondent: Containing, New Elucidations, Discoveries ...

George Baron - 1804 - 318 σελίδες
...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...

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

Robert Simson - 1806 - 546 σελίδες
...' when the less is *•- v"~* • contained a certain number of times exactly in the greater,' II. A greater magnitude is said to be a multiple of a...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...

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

John Playfair - 1806 - 320 σελίδες
...greater, that is, when the less is contained a certain number of 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 greater contains the less a certain number of...

A Course of Mathematics ...: Designed for the Use of the Officers ..., Τόμος 1

Isaac Dalby - 1807 - 476 σελίδες
...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...

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

Sir John Leslie - 1809 - 522 σελίδες
...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...

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

Euclid - 1810 - 554 σελίδες
...greater, that is, ' when the less • is contained a certain number of times exactly in the greater.' II. A greater magnitude is said to be a multiple of a...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...

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

John Mason Good - 1813 - 714 σελίδες
...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...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 σελίδες
...is,' when s -*v"*' ' the less is contained a certain number of times exactly ' in the greater." II. A greater magnitude is said to be a multiple of a...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...

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

Euclides - 1816 - 588 σελίδες
...that is, 'when ^v-" * the less is contained a certain number of times exactly ' in the greater.' II. A greater magnitude is said to be a multiple of a...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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