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" If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion. "
First Lessons in Geometry: Upon the Model of Colburn's First Lessons in ... - Page 24
by Alpheus Crosby - 1847 - 164 pages
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...given, — =6; if a, b, and c, are given, — =d; and be if d, b, and c, are given, then -r=a '• 60. If the product of two quantities be equal to the product of two others, then if the terms of one product be made the means, and the terms of the other product the...
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The Elements of Algebra: Designed for the Use of Students in the University

James Wood - Algebra - 1815 - 338 pages
...three terms in a proportion being given, the fourth may be determined from the equation ad=bc. (175.) If the product of two quantities be equal to the product of two others, the four are proportionals, making the terms of one product the means, and the terms of the...
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The Complete Practical Arithmetician: Containing Several New and Useful ...

Thomas Keith - Arithmetic - 1822 - 354 pages
...their numerators are equal, therefore AD=BC; A and D being the extremes, and B and c the means. 12. If the product of two quantities be equal to the product of two others, the four quantities may be turned into a proportion, by making the terms of one product the...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...and, therefore, x = Vac. » 110. The converse of each of the preceding theorems is also true, that is, If the product of two quantities be equal to the product of two others, or if the product of two be equal to the square of one, then the FOUR, or the THREE quantities...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...greater than C, thenB is greater than D,if A=C,thenB=D,andif A be less than C, then B is less than D. 33. If the product of two quantities be equal to the product of two other quantities, these four quantities may be turned into a proportion by making the terms of one product the means,...
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The student's algebra

John Darby (teacher of mathematics.) - 1829 - 212 pages
...b ; ' c ; d, then will ad = be. Also, if a ; 6 ; rb ; c, then will ac = 62. Whence it follows, that if the product of two quantities be equal to the product of two other quantities, the four quantities will be proportionals, thus, ad=bc, and this is turned into a proportion by making...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...4.), the product of the extremes will be equal to the square of the mean. PROPOSITION II. THEOREM. If the product of two quantities be equal to the product of two other quantities, two of them will be the extremes and the other two the means of a proportion. Let Mx Q=NxP ; then will M: N : :...
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The mechanical Euclid, containing the elements of mechanics and hydrostatics

William Whewell - 1837 - 226 pages
...product of the extremes is equal to the square of the mean. For (Art. 39) if a : x :: x : 6, ab = a?. 41. If the product of two quantities be equal to the product of two others, the four are proportionals, making the terms of one product the means, and the terms of the...
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An Elementary Treatise on Algebra, Theoretical and Practical: With Attempts ...

John Radford Young - 1839 - 332 pages
...proportionate, then - = -; multiply each side и С by ас, and there results be — ad. THEOREM 2. If the product of two quantities be equal to the product of two others, then a proportion may be formed of the four quantities. Let qr = ps ; then, dividing each side...
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The Elements of Algebra

Thomas Grainger Hall - 1840 - 266 pages
...quantities be proportionals the product of the extremes equals the product of the means ; and conversely, if the product of two quantities be equal to the product of other two quantities, the four are proportionals. For let ad = bc, then divide both sides by bd ; ac...
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