Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1834 Excerpt: ... the time allowed, the less will be the number of men required to do the work, we shall have the following proportion; 8: 6 = 32: A, and this gives 24 men for the fourth term, which is the answer to the question. We see in this solution, that 16 is multiplied by 135, and the product divided by 54; the quotient, being made the third term in the second proportion, is multiplied by 4, and the product divided by 5; this last quotient, being made the third term in the third proportion, is multiplied by 6, and the product divided by 8. Theresuit, therefore, would be the same, if 135 and 4 and 6 were multiplied together, and their product multiplied by 16, and this last product divided by the product of 54 and 5 and 8. The proportion may be thus arranged. 54: 135) 5: 4 = 16: A 8: 6) 2160: 3240 =16: A If, instead of calculating the fourth term in each proportion, we only indicate the operation by a fraction, we shall have, in the first of the foregoing proportions, T--for tne fourth term: taking this for the third term of the second proportion, we shall have the following, 5: 4 =-: A, and the fourth term will be--5 taking this for the third term in the third proportion, we shall have the following, 8:6 = 165x4: A, and the fourth term will be 16f548x6, which is equal to 24, the number of men required. In this fractional expression, we see at once, that the product of all the second terms is multiplied by the third term, and that this product is divided by the product of all the first terms, and the quotient is the fourth term, or answer to the question. Hence we see, that questions in compound proportion will be accurately solved by the following rule. RULE. Make the number, which is of the same kind with the answer, the third term; of the remaining numbers, take an...
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Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1834 Excerpt: ... the time allowed, the less will be the number of men required to do the work, we shall have the following proportion; 8: 6 = 32: A, and this gives 24 men for the fourth term, which is the answer to the question. We see in this solution, that 16 is multiplied by 135, and the product divided by 54; the quotient, being made the third term in the second proportion, is multiplied by 4, and the product divided by 5; this last quotient, being made the third term in the third proportion, is multiplied by 6, and the product divided by 8. Theresuit, therefore, would be the same, if 135 and 4 and 6 were multiplied together, and their product multiplied by 16, and this last product divided by the product of 54 and 5 and 8. The proportion may be thus arranged. 54: 135) 5: 4 = 16: A 8: 6) 2160: 3240 =16: A If, instead of calculating the fourth term in each proportion, we only indicate the operation by a fraction, we shall have, in the first of the foregoing proportions, T--for tne fourth term: taking this for the third term of the second proportion, we shall have the following, 5: 4 =-: A, and the fourth term will be--5 taking this for the third term in the third proportion, we shall have the following, 8:6 = 165x4: A, and the fourth term will be 16f548x6, which is equal to 24, the number of men required. In this fractional expression, we see at once, that the product of all the second terms is multiplied by the third term, and that this product is divided by the product of all the first terms, and the quotient is the fourth term, or answer to the question. Hence we see, that questions in compound proportion will be accurately solved by the following rule. RULE. Make the number, which is of the same kind with the answer, the third term; of the remaining numbers, take an...
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