William Oughtred invented the Slide Rule

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Just Before the Slide Rule Galileo Galilei popularizes the sector at the very end of the 16th Century. Clavis mathematicae, 1652 William Oughtred became especially famous for an early version of the slide rule. The most eye-catching feature on the new 38mm is the slide rule, especially on the blue dial variant, which appears clearer without the sub-dials. Much of the advanced mathematics of the age was devoted to astronomy and the trigonometry involved with laying out accurate sundials, hence the slide rule and timekeeping have been linked since the beginning.

One end has an extension about 1. In 1619, John Napier discovered the ultimate number-crunching cheat-code: the logarithm.

Slide rule

At the turn of the 16th century, Johannes Kepler set out to disprove Copernicus, who believed planets orbited in perfect, concentric circles from the sun. Kepler first formulated his hypothesis: planets had elliptical orbits with two foci, and then set out to prove it mathematically. But it was who invented the slide rule that Kepler managed it — his calculations were riddled with mistakes. Only after repeating his procedures 70 times did he offset his computational errors. How many Keplers weren't so fortunate. For most of history, basic calculations were a serious bottleneck to science. A great deal of people, throughout history, have spent a great deal of time coming up with tricks to do it faster. Millennia of their work culminated in the greatest mechanical calculating device there is: the slide rule. Multiplying is hard, but adding is easy. This is the core insight underpinning most number-crunching tricks and, as we'll see, the slide rule. They realized they could do multiplications once, and write the results on a cheat-sheet to avoid having to do them again. But when your cheat-sheet is more of a cheat-stone-tablet, every result matters. The next hack came through mathematical identities — cheat codes to express one calculation in terms of another. The Babylonians came up with many of these. A classic is the quarter-square multiplication, which reduces multiplication to subtraction. On the face of it, this looks a lot more complicated than just multiplying the damn numbers. Pre-computing just 24 results now lets us multiply any two numbers between 1 and 12. We need — who invented the slide rule — to store fewer results. Thousands of years later, the solution finally arrived. In 1619, John Napier discovered the ultimate number-crunching cheat-code: the logarithm. Pierre-Simon Laplace, to whom we owe much of physics and statistics, wrote:. We all know that multiplying powers of 10 is easy — we just add the number of zeros: This is actually just a clever application of logarithms. If we can understand how it works, we can generalize it for all numbers. The number of zeros is a special quantity that lets us turn multiplication into addition, but it only works for powers of 10. Is there an equivalent quantity for other numbers. So the equivalent for, say, powers of 2, would be the number of 2s multiplied together. In the world of 10s, the logarithm of x tells you how many times you have to multiply 10 by itself to get that x. In the world of 2s, log x tells you how many times you have to multiply 2 by itself to get x. By converting numbers into their logarithms, we can turn multiplication into addition. If we had two sticks with linear scales, we could use them to add numbers together. Suppose you slide the top stick by a distance of 1 unit. The bottom stick will now show the result of adding 1 to each number on the top stick. If we had two sticks with logarithmic scales, we could use them to add logarithms together in the same way. But as we know, adding logarithms lets us multiply numbers. Suppose you slide the top stick by a distance of log 2. The bottom stick will now show the result of multiplying by 2 each number on the top stick. Different calculations can be carried out by sliding the sticks by different amounts. As time went on, the device gained more and more bells and whistles allowing it to do more and more things. The first problem was multiplying bigger and bigger numbers. Doing this without making the slide rule longer required more and more precision on the scales, the equivalent of having millimeters and tenths-of-millimeters on a centimeter rule. A movable pointer called a cursor was developed to make it easier to read numbers off more precisely. Next, people wanted to do more than just multiplication. Different scales were developed for squares, square roots, trigonometric functions, their hyperbolic equivalents, and an array of niche functions corresponding to specific applications. The standard slide rule eventually had 6 different scales for different functions. And they even devised algorithms to solve more complex problems, like, and. The slide rule is an elegant piece of mathematics represented in an equally elegant physical representation. In spite of its simplicity, the slide rule is all around us — it's designed major structures in modern history, and taken us to the moon. Taimur Abdaal Product, Growth, Writing.

Slide rule, a device consisting of graduated scales capable of relative movement, by means of which simple calculations may be carried out mechanically. Keep in mind, that same amount would buy two brand new cars in 1968. Only after repeating his procedures 70 times did he offset his computational errors. Addition and subtraction steps in a calculation are done mentally or on paper, not on the slide rule. Practically overnight, the slide rule had become obsolete. The most popular were trigonometric, usually sine and tangent, common logarithm log10 for taking the log of a value on a multiplier scale , natural logarithm ln and exponential ex scales. In the next fifty years they increase from three, to six, to eight scales on the slide rule, as engineering extends its grip on modern computation. The recommended cleaning method for engraved markings is to scrub lightly with steel-wool. The Keuffel and Esser rules from the period up to about 1950 are particularly problematic, because the end-pieces on the cursors tend to break down chemically over time. With slide rules, there was a great emphasis on working the algebra to get expressions into the most computable form. As an anecdote it can be mentioned that German rocket scientist Wernher von Braun brought two 1930s vintage Nestler slide rules with him when he moved to the U.