 | Charles Butler - 1814 - 528 σελίδες
...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... | |
 | James Wood - 1815 - 338 σελίδες
...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... | |
 | Thomas Keith - 1822 - 354 σελίδες
...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... | |
 | George Lees - 1826 - 276 σελίδες
...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... | |
 | John Playfair - 1829 - 210 σελίδες
...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,... | |
 | John Darby (teacher of mathematics.) - 1829 - 212 σελίδες
...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... | |
 | Adrien Marie Legendre - 1836 - 394 σελίδες
...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 : :... | |
 | William Whewell - 1837 - 226 σελίδες
...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... | |
 | John Radford Young - 1839 - 332 σελίδες
...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... | |
 | Thomas Grainger Hall - 1840 - 266 σελίδες
...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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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. 
