Logarithms who invented

We can summarize Napier's explanation as follows Descriptio I, 1 p. Figure 3. The relation between the two lines and the logs and sines. Napier generated numerical entries for a table embodying this relationship.

However in terms of the way he actually computed these entries, he would have in fact worked in the opposite manner, generating the logarithms first and then choosing those that corresponded to a sine of an arc, which accordingly formed the argument.

The values in the first column in bold that corresponded to the Sines of the minutes of arcs third column were extracted, along with their accompanying logarithms column 2 and arranged in the table.

The appropriate values from Table 1 can be seen in rows one to six of the last three columns in Figure 4. The excerpt in Figure 4 gives the first half of the first degree and, by symmetry, on the right the last half of the eighty-ninth degree. To complete the tables, Napier computed almost ten million entries from which he selected the appropriate values. Napier himself reckoned that computing this many entries had taken him twenty years, which would put the beginning of his endeavors as far back as Figure 4.

Napier frequently demonstrated the benefits of his method. For example, he worked through a problem involving the computation of mean proportionals, sometimes known as the geometric mean.

He stated:. Let the extremes and bee given, and let the meane proportionall be sought: that commonly is found by multiplying the extreames given, one by another, and extracting the square root of the product. But we finde it earlier thus; We adde the Logarithme of the extreames 0 and , the summe whereof is which we divide by 2 and the quotient shall be the Logar. By which the middle proportionall , and his arch 45 degrees are found as before Book I, 5 p. Kathleen M. Skip to main content. Search form Search.

Login Join Give Shops. Halmos - Lester R. Ford Awards Merten M. Author s :. John Napier from MacTutor History of Mathematics Archive Napier first published his work on l ogarithms in under the title Mirifici logarithmorum canonis descriptio, which translates literally as A Description of the Wonderful Table of Logarithms. A logarithm can be thought of as the inverse of an exponential, so the above equation has the same meaning as:. This means if we fold a piece of paper in half six times, it will have 64 layers.

Understanding that 1 ml of pure alcohol has roughly 10 22 a one followed by 22 zeroes molecules, how many C dilutions will it take until all but one molecule is replaced by water?

Thus, after 11 C dilutions, there will only be one molecule of the original alcohol left. Aside, this is less than half of the 30 C dilutions common in homeopathy, which shows why the practice is irreconcilable with modern chemistry.

Most scientific calculators only calculate logarithms in base 10, written as log x for common logarithm and base e , written as ln x for natural logarithm the reason why the letters l and n are backwards is lost to history. The number e , which equals about 2. To do a logarithm in a base other than 10 or e , we employ a property intrinsic to logarithms. Because logarithms relate multiplicative changes to incremental changes, logarithmic scales pop up in a surprising number of scientific and everyday phenomena.

The table shows that the numbers relating various linear and logarithmic systems vary widely. This is because a logarithmic scale is often invented first as a characterization technique without a deep understanding of the measurable phenomena behind that characterization.

A good example is star brightness, which was introduced by Hipparchus, a second-century B. Greek astronomer. In the 19th century A. Most other logarithmic scales have a similar story. That logarithmic scales often come first suggests that they are, in a sense, intuitive.

This not only has to do with our perception, but also how we instinctively think about numbers. Though logarithmic scales are troublesome to many if not most math students, they strangely have a lot to do with how we all instinctively thought about numbers as infants.