Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση
[ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]
[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small]

31. A number is formed of two digits. The sum of the squares of the digits is 58. If 12 times the units' digit is subtracted from the number, the order of the digits will be reversed. Find the number.

32. A rectangular garden is surrounded by a walk 7 feet wide. The area of the garden is 15,000 square feet, and of the walk 3696 square feet. Find the dimensions of the garden.

33. The sum of two numbers is 9, and the sum of their cubes is 243. Find the numbers.

34. The difference between the areas of two squares is 231 square inches. The difference between their perimeters is 28 inches. Find their sides.

35. The hypotenuse of a right triangle is 20 inches and the area of the triangle is 96 square inches. Determine the legs.

36. If the difference of two numbers multiplied by the greater is 160, and multiplied by the less, is 96, find the numbers.

CHAPTER XIX

LOGARITHMS

150. The logarithm of any number is the exponent of the power to which a fixed number must be raised to equal the given number. The fixed number is called the base of the system of logarithms.

The Briggs or Common system of logarithms uses the number 10 as its base. Hence, the common logarithm of any number is the exponent of the power to which 10 is raised to equal the given number. Thus since 100 = 102, the logarithm of 100 is 2, which is written, log 100 = 2. In this book, the common system of logarithms only is used.

[blocks in formation]

Hence, the logarithms of numbers greater than 1 are positive, and the logarithms of numbers less than 1 are negative. Also, since most numbers are not an integral power of 10, the logarithms of such numbers are not integers, but mixed numbers, consisting of an integral part and a fraction. This fractional part of the logarithm is usually expressed as a decimal.

[merged small][merged small][graphic][merged small]

(From an Engraving After an Original Edinburgh Painting)
Born near Edinburgh, 1550. Died, 1617.
Inventor of logarithms.

His Mirifici logarithmorum canonis descriptio (1614), the first important work on mathematics produced in Great Britain, inspired Briggs to develop the common system of logarithms with the decimal base.

Napier was a student of theology and astrology, engaging in many controversies.

The great object of his mathematical studies was to simplify and systematize arithmetic, algebra and trigonometry.

Napier succeeded in constructing a system of logarithms before exponents were used.

« ΠροηγούμενηΣυνέχεια »