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#### In my view, the Christian religion is the most important and one of the first things in which all children, under a free government ought to be instructed... No truth is more evident to my mind than that the Christian religion must be the basis of any government intended to secure the rights and privileges of a free people. - Preface

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 Word Definition

1828.mshaffer.comWord [logarithm]

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# logarithm

LOG'ARITHM, n. [Gr. ratio, and number.]

Logarithms are the exponents of a series of powers and roots.

The logarithm of a number is that exponent of some other number, which renders the power of the latter, denoted by the exponent, equal to the former.

When the logarithms form a series in arithmetical progression, the corresponding natural numbers form a series in geometrical progression. Thus,

Logarithms
0 1 2 3 4 5

Natural numbers, 1 10 100 1000 10000 100000

The addition and subtraction of logarithms answer to the multiplication and division of their natural numbers. In like manner, involution is performed by multiplying the logarithm of any number by the number denoting the required power; and evolution, by dividing the logarithm by the number denoting the required root.

Logarithms are the invention of Baron Napier, lord of Marchiston in Scotland; but the kind now in use, were invented by Henry Briggs, professor of geometry in Gresham college at Oxford. They are extremely useful in abridging the labor of trigonometrical calculations.

## Evolution (or devolution) of this word [logarithm]

1828 Webster1844 Webster1913 Webster

LOG'ARITHM, n. [Gr. ratio, and number.]

Logarithms are the exponents of a series of powers and roots.

The logarithm of a number is that exponent of some other number, which renders the power of the latter, denoted by the exponent, equal to the former.

When the logarithms form a series in arithmetical progression, the corresponding natural numbers form a series in geometrical progression. Thus,

Logarithms
0 1 2 3 4 5

Natural numbers, 1 10 100 1000 10000 100000

The addition and subtraction of logarithms answer to the multiplication and division of their natural numbers. In like manner, involution is performed by multiplying the logarithm of any number by the number denoting the required power; and evolution, by dividing the logarithm by the number denoting the required root.

Logarithms are the invention of Baron Napier, lord of Marchiston in Scotland; but the kind now in use, were invented by Henry Briggs, professor of geometry in Gresham college at Oxford. They are extremely useful in abridging the labor of trigonometrical calculations.

LOG'A-RITHM, n. [Fr. logarithme; Gr. λογος, ratio, and αριθμος, number.]

Logarithms are the exponents of a series of powers and roots. – Day. The logarithm of a number is that exponent of some other number, which renders the power of the latter, denoted by the exponent, equal to the former. – Cyc. When the logarithms form a series in arithmetical progression, the corresponding natural numbers form a series in geometrical progression. Thus, Logarithms, 0 1 2 3 4 5 Natural numbers, 1 10 100 1000 10000 100000 The addition and subtraction of logarithms answer to the multiplication and division of their natural numbers. In like manner, involution is performed by multiplying the logarithm of any number by the number denoting the required power; and evolution, by dividing the logarithm by the number denoting the required root. Logarithms are the invention of Baron Napier, lord of Marchiston in Scotland; but the kind now in use, were invented by Henry Brigs, professor of geometry in Gresham college, at Oxford. They are extremely useful in abridging the labor of trigonometrical calculations.

Log"a*rithm
1. One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland (1550-1617), to abridge arithmetical calculations, by the use of addition and subtraction in place of multiplication and division.

The relation of logarithms to common numbers is that of numbers in an arithmetical series to corresponding numbers in a geometrical series, so that sums and differences of the former indicate respectively products and quotients of the latter; thus,

```
0    1    2     3      4       Indices or logarithms
1   10   100  1000  10,000     Numbers in geometrical
progression
```

Hence, the logarithm of any given number is the exponent of a power to which another given invariable number, called the base, must be raised in order to produce that given number. Thus, let 10 be the base, then 2 is the logarithm of 100, because 102 = 100, and 3 is the logarithm of 1,000, because 103 = 1,000.

Arithmetical complement of a logarithm, the difference between a logarithm and the number ten. -- Binary logarithms. See under Binary. -- Common logarithms, or Brigg's logarithms, logarithms of which the base is 10; -- so called from Henry Briggs, who invented them. -- Gauss's logarithms, tables of logarithms constructed for facilitating the operation of finding the logarithm of the sum of difference of two quantities from the logarithms of the quantities, one entry of those tables and two additions or subtractions answering the purpose of three entries of the common tables and one addition or subtraction. They were suggested by the celebrated German mathematician Karl Friedrich Gauss (died in 1855), and are of great service in many astronomical computations. -- Hyperbolic, or Napierian, logarithms, those logarithms (devised by John Speidell, 1619) of which the base is 2.7182818; -- so called from Napier, the inventor of logarithms. -- Logistic or Proportionallogarithms., See under Logistic.

1828 Webster1844 Webster1913 Webster

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Logarithm

LOG'ARITHM, noun [Gr. ratio, and number.]

Logarithms are the exponents of a series of powers and roots.

The logarithm of a number is that exponent of some other number, which renders the power of the latter, denoted by the exponent, equal to the former.

When the logarithms form a series in arithmetical progression, the corresponding natural numbers form a series in geometrical progression. Thus,

Logarithms

0 1 2 3 4 5

Natural numbers, 1 10 100 1000 10000 100000

The addition and subtraction of logarithms answer to the multiplication and division of their natural numbers. In like manner, involution is performed by multiplying the logarithm of any number by the number denoting the required power; and evolution, by dividing the logarithm by the number denoting the required root.

Logarithms are the invention of Baron Napier, lord of Marchiston in Scotland; but the kind now in use, were invented by Henry Briggs, professor of geometry in Gresham college at Oxford. They are extremely useful in abridging the labor of trigonometrical calculations.

### Why 1828?

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In studying Gods Word , it give a greater understanding to the Scriptures.

— JAY (Bessemer City, NC)

### Word of the Day

IMPORT'ANCE, n.

1. Weight; consequence; a bearing on some interest; that quality of any thing by which it may affect a measure, interest or result. The education of youth is of great importance to a free government. A religious education is of infinite importance to every human being.

2. Weight or consequence in the scale of being.

Thy own importance know.

Nor bound thy narrow views to things below.

3. Weight or consequence in self-estimation.

He believes himself a man of importance.

4. Thing implied; matter; subject; importunity. [In these senses, obsolete.]

### Random Word

1. Lightly; inconsiderably; in a trifling degree.

### Noah's 1828 Dictionary

First dictionary of the American Language!

Noah Webster, the Father of American Christian education, wrote the first American dictionary and established a system of rules to govern spelling, grammar, and reading. This master linguist understood the power of words, their definitions, and the need for precise word usage in communication to maintain independence. Webster used the Bible as the foundation for his definitions.

This standard reference tool will greatly assist students of all ages in their studies.

No other dictionary compares with the Webster's 1828 dictionary. The English language has changed again and again and in many instances has become corrupt. The American Dictionary of the English Language is based upon God's written word, for Noah Webster used the Bible as the foundation for his definitions. This standard reference tool will greatly assist students of all ages in their studies. From American History to literature, from science to the Word of God, this dictionary is a necessity. For homeschoolers as well as avid Bible students it is easy, fast, and sophisticated.

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