Fundamentals of high school mathematics; a textbook designed to follow arithmetic

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. 1919 Excerpt: ...nature. The examples in the following exercises will illustrate what is meant by opposite qualities, or numbers of opposite nature. We shall take four different kinds of illustrations: (1) opposite numbers on a temperature scale, (2) opposite numbers on a distance scale, (3) opposite numbers to represent financial situations ("having" and "owing "), (4) opposite numbers on a time scale, to represent "time before" a beginning point and "time after." FIRST ILLUSTRATION: OPPOSITE NUMBERS ON A TEMPERATURE SCALE EXERCISE 56 1. The top of the mercury column of a thermometer stands at zero degrees (0). During the next hour.it rises 3, and the next it rises 4. What is the temperature at the end of the second hour? 2. The top of the mercury column stands at 0. During the next hour it falls 3, and in the next it falls 4. What is the reading at the end of the second hour? 3. If it starts at 0, rises 3, and then falls 4, what is the reading? 4. If it starts at 0, falls 3, and then rises 4, what is the reading? These examples show that we must distinguish two kinds of temperature readings, (1) those above zero and (2) those below zero. People have agreed to call readings above zero POSITIVE, and readings below zero NEGATIVE. Thus, if the mercury starts at zero and rises 4, it will be at positive 4, or, more briefly, + 4. But if it starts at zero and falls 4, it will be at negative 4, or--4. In the remainder of these examples you should describe the mercury readings as positive or negative, rather than as above or below zero. 5. The temperature stands at zero. Its first change is described by the expression + 6. Its next change is described by + 4. What is the temperature at the end of the second change? 6. If the temperature readi...