 | John William Hopkins, Patrick Healy Underwood - 1912 - 406 páginas
...quantities given. These four quantities will then form a proportion which can be solved by placing the product of the means equal to the product of the extremes. It is well to state a problem so that one can see all around it ; eg 12 men do the work in 15 da. 9 men do... | |
 | Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - 1912 - 494 páginas
...4^=^Az S22 But si=what? Therefore si2=what? Substitute this value of si2 in the proportion and take the product of the means equal to the product of the extremes. Write the following law: The area of any regular polygon equals the square of one of its sides multiplied... | |
 | Clara Avis Hart, Daniel D. Feldman - 1912 - 504 páginas
...algebra are usually simplified by this process, so, also, proportions may be simplified by placing the product of the means equal to the product of the extremes. 390. Cor. I. The mean proportional' between two numbers is equal to the square root of their product.... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - 1915 - 336 páginas
...hypotenuse equals the sum of the squares of the two sides. Proof. In each proportion of § 435, take the product of the means equal to the product of the extremes. Then o? = a'c and 62 = b'c. Adding, a2 + b2 = (a'+b') c. But a'-\-b' = c. 439. Theorem. A perpendicular... | |
 | George Johnson - 1916 - 64 páginas
...as the greatest is to the third from it so is the second, next to it, to the fourth, for this makes the product of the means equal to the product of the extremes ; now again if the difference between the greatest and the term next to it can be shown to be equal... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 460 páginas
...hypotenuse equals the sum of the squares of the two sides. Proof. In each proportion of § 435, take the product of the means equal to the product of the extremes. Then a2 = a'c and b- = b'c. Adding, a2+62=(a'+6')c. But a'+b' = c. 439. Theorem. A perpendicular drawn... | |
 | 1918 - 840 páginas
...by 4 feet by 20 feet. This is reduced to the simple proportion, 144 x : 3456 : : 3600 : 4800. Making the product of the means equal to the product of the extremes, the value of x is found to be 18. Answer, 18 men. SQUARE AND CUBE ROOT. X The square of a number is... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - 1920 - 390 páginas
...Solution of Proportions. Ex. 1. Find the value of x in the proportion 2x+3 : 3x-l=3x + l : 2x+l. Taking the product of the means equal to the product of the extremes Hence, x =2, - f. Ans. Ex. 2. What number added to each of the numbers 5, 8, 11, and 16 will give results... | |
 | Julius J. H. Hayn - 1925 - 328 páginas
...to the fourth. Hyp.: Given that a : b = c : d. Det.: To prove that a : c = b : d. Proof: By taking the product of the means equal to the product of the extremes, we have be = ad, or ad = be. Dividing both sides by cd. we have —; = —r. ° r — = —r • ~.... | |
 | Nicomachus (of Gerasa.), Frank Egleston Robbins, Louis Charles Karpinski - 1926 - 348 páginas
...medielas, quae inter utrasqiK versatur, deesse non possil. it to the fourth; for such a situation makes the product of the means equal to the product of the extremes. And again, if the greatest term be shown to differ from the one next beneath it by the amount whereby... | |
| |
But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect... 
