Books Books A greater magnitude is said to be a multiple of a less, when the greater is measured by the less ; that is, ' when the greater contains the less a certain number of times exactly.' 3. ' Ratio is a mutual relation of two magnitudes of the same kind to... Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ... - Page 89
by John Mason Good - 1813 ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...mutual relation of two magnitudes of the same kind Ste N ' to one another, in respect of quantity.' IV. Magnitudes are said to have a ratio to one another,...less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the second, which the third has to... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...the less, that is, when the greater contains the less a certain number of times exactly. III. Ratio is a mutual relation of two magnitudes, of 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... ## A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 1

Isaac Dalby - Mathematics - 1807
...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 ...

Sir John Leslie - Geometry, Analytic - 1809 - 524 pages
...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 ...

Euclides - 1816 - 528 pages
...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 another,...less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same ratio to the second, which the third has to... ## Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...ratios. • DEF. IV. This definition is a little altered in the expression : Euclid has it, that " magnitudes are said to have a ratio to one another,...the -" less can be multiplied so as to exceed the greater." DEF. V. One of the chief obstacles to the ready understanding of the 5tU Book of Euclid,... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...the less, that is, when the greater contains the less a certain number of times exactly. HI. Ratio is a mutual relation of two magnitudes, of the same kind, to one another, in respect of quantity. IV. Magnitudes are said to be of the same kind, when the less can be multiplied so as to exceed the... ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 516 pages
...less, that is, 'when the greater contains the less a certain number of times exactly.' III. ' Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.'* IV. Magnitudes are said to have a ratio to one another, when the less can be multiplied so as to exceed... ## The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821
...less measures it. 3. Ratio is the mutual relation of two magnitudes of the same kind, with respect to quantity. 4. Magnitudes are said to have a ratio to one another, •when they are such that the less can be multiplied so as to exceed the greater. Note. All commensurable... 