[This Southern algebra textbook, published in 1857, illustrates the hate that some residents of the South had for those in the North. The person who gave the glowing review is now better known as Confederate General "Stonewall" Jackson.]

## Testimonials.

From T. J. Jackson, Professor of Natural and Experimental Philosophy, Virginia Military Institute.

“From an examination of various portions of Major D. H. Hill’s Algebra, in manuscript, I regard it as superior to any other work with which I am acquainted on the same branch of science.”

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## Negative Quantities

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19. Milk sells in the City of New York at 4 cents per quart. A milkman mixed some water with 50 gallons of milk, and sold the mixture at 3 cents per quart without sustaining any loss by the sale. How much water did he put in the milk? *Ans*. 66 2/3 quarts.

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40. A Yankee mixes a certain number of wooden nutmegs, which cost him ¼ cent apiece, with a quantity of real nutmegs, worth 4 cents apiece, and sells the whole assortment for $44; and gains $3.75 by the fraud. How many wooden nutmegs were there? *Ans*. 100.

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44. A northern railroad company is assessed $120,000 damages for contusions and broken limbs, caused by a collision of cars. They pay $5000 for each contusion, and $6000 for each broken limb; and the entire amount paid for bruises and fractures is the same. How many persons received contusions, and how many had their limbs broken? *Ans*. 12 of the former, and 10 of the latter.

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70. At the Woman’s Rights Convention, held at Syracuse, New York, composed of 150 delegates, the old maids, childless-wives, and bedlamites were to each other as the numbers 5, 7, and 3. How many were there of each class? *Ans*. 50, 70, and 30.

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## Elimination Between Simultaneous Equations of the First Degree

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14. In the year 1692, the people of Massachusetts executed, imprisoned, or privately persecuted 469 persons, of both sexes, and all ages, for the alleged crime of witchcraft. Of these, twice as many were privately persecuted as were imprisoned, and 7 17/19 times as many more were imprisoned than were executed. Required the number of sufferers of each kind? *Ans*. 19 executed, 150 imprisoned, and 300 privately persecuted.

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## Equations of the Second Degree

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25. The year in which Decatur published his official letter from New London, stating that the traitors of New England burned blue lights on both points of the harbour to give notice to the British of his attempt to go to sea, is expressed by four digits. The sum of the first and fourth is equal to half the second; the first and third are equal to each other; the sum of the first and second is equal to three times the fourth, and the product of the first and second is equal to 8. Required the year. *Ans*. 1813.

26. The year in which the Governors of Massachusetts and Connecticut sent treasonable messages to their respective Legislatures, is expressed by four digits. The square root of the sum of the first and second is equal to 3; the square root of the product of the second and fourth is equal to 4; the first is equal to the third, and is one-half of the fourth. Required the year. *Ans*. 1812.

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28. Some of the New England States were fully, and some partially, represented in the Hartford Convention, which, in the year 1814, gave aid and comfort to the British during the progress of the war. If 4 be added to the number of States fully and partially represented, and the square root of the sum be taken, the result will be the number of States fully represented; but if 11 be added to the sum of the States fully and partially represented, and the square root of the sum be taken, the result will be equal to the square root of 8 times the number of States partially represented. Required the number of States fully and partially represented. *Ans*. Three fully represented; two partially represented.

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36. In the year 1637, all the Pequod Indians that survived the slaughter on the Mystic River were either banished from Connecticut, or sold into slavery. The square root of twice the number of survivors is equal to 1/10th that number. What was the number? *Ans*. 200.

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39. In the year 1853, a number of persons in New England and New York, were sent to lunatic asylums in consequence of the Spiritual Rapping delusion. If 14 be added to the number of those who became insane, and the square root of the sum be taken, the root will be less than the number by 42. Required the number of victims. *Ans*. 50.

Why is the second value of *x* rejected ?

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45. In the year 1706 the French made a descent upon Charleston; but “South Carolina,” says Bancroft, “gloriously defended her territory, and, with very little loss, repelled the invaders.” A certain number of the French were killed and wounded, and 100 were taken prisoners. The number of killed and wounded was to the number of uninjured, including the prisoners, as 1 to 3. And the square of the number that escaped in safety from the expedition, was to the square of the number killed and wounded, as 6¼ to 1. Required the number of invaders, and the number of killed and wounded. *Ans*. 800 invaders, and 200 killed and wounded.

Verification. If 200 were killed and wounded, then 600 were uninjured, and 200 : 600 :: 1 : 3. And, since 100 were taken prisoners, 500 escaped without harm from the expedition, and (500)² : (200)² :: 6¼ : 1.

Why is the value connected with the negative sign of the radical rejected?

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47. A man in Cincinnati purchased 10,000 pounds of bad pork, at 1 cent per pound, and paid so much per pound to put it through a chemical process, by which it would appear sound, and then sold it at an advanced price, clearing $450 by the fraud. The price at which he sold the pork per pound, multiplied by the cost per pound of the chemical process, was 3 cents. Required the price at which he sold it, and the cost of the chemical process. *Ans*. He sold it at 6 cents per pound, and the cost of the process was ½ cent per pound.

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52. The field of battle at Buena Vista is 6½ miles from Saltillo. Two Indiana volunteers ran away from the field of battle at the same time; one ran half a mile per hour faster than the other, and reached Saltillo 5 minutes and 54 6/11 seconds sooner than the other. Required their respective rates of travel. *Ans*. 6, and 5½ miles per hour.

[There are no problems in the book portraying Southerners in a negative light. However, there are several problems involving Southerners working slaves for long hours, such as:]

## Geometrical Proportion

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10. A planter, who knows that his negro-man can do a piece of work in 5 days, when the days are 12 hours long, asks how long it will take him when the days are 15 hours long. *Ans*. 4 days.