 | 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 extremes,... | |
 | 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...the means, and the terms of the other, the extremes. x "h Let xy — ab, then dividing by ay, - = -, or x : a :: . <•* y b :y. (Art. 171). • 076.) /f... | |
 | 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 means, and the terms... | |
 | James Wood - Algebra - 1825 - 322 pages
...being given, the fourth may be determined from the equation ad = bc. (175.) If the product of taso quantities be equal to the product of two others,...the means, and the terms of the other, the extremes. Let xy = ab, then dividing by ay, - = -, or x : a :: b:y. (Art. 171). (176.) If a : b :: с : d, and... | |
 | Thomas Keith - Arithmetic - 1825 - 360 pages
...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 means, and the terms of the other the extremes, Thus, if AD=BC, divide each by BD, then — = — ' BD BD . AC viz. - =- , or A : B : : c : D. BD 13.... | |
 | 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 will... | |
 | Thomas Kerigan - Nautical astronomy - 1828 - 776 pages
...extremes, viz. 16 x 2, is equal to the rectangle of the means, viz. 4x8, or 32. If the product of any 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 means, and the terms... | |
 | 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... | |
 | 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... | |
 | 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... | |
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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. 
