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4586:. "With computation moving literally at a hand's pace and the lack of precision a given, mathematicians worked to simplify complex problems. Because linear equations were friendlier to slide rules than more complex functions were, scientists struggled to linearize mathematical relations, often sweeping high-order or less significant terms under the computational carpet. So a car designer might calculate gas consumption by looking mainly at an engine's power, while ignoring how air friction varies with speed. Engineers developed shortcuts and rules of thumb. At their best, these measures led to time savings, insight and understanding. On the downside, these approximations could hide mistakes and lead to gross errors."
4603:. "One effect was that users felt close to the numbers, aware of rounding-off errors and systematic inaccuracies, unlike users of today's computer-design programs. Chat with an engineer from the 1950s, and you will most likely hear a lament for the days when calculation went hand-in-hand with deeper comprehension. Instead of plugging numbers into a computer program, an engineer would understand the fine points of loads and stresses, voltages and currents, angles and distances. Numeric answers, crafted by hand, meant problem solving through knowledge and analysis rather than sheer number crunching."
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4569:, Barbara Duch, Susan Groh, Deborah Allen, eds., Stylus Publishing, LLC, 2001. "Numerical computations in freshman physics and chemistry were excruciating; however, this did not seem to be the case for those students fortunate enough to already own a calculator. I vividly recall that at the end of 1974, the students who were still using slide rules were given an additional 15 minutes on the final examination to compensate for the computational advantage afforded by the calculator, hardly adequate compensation in the opinions of the remaining slide rule practitioners."
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operations that were easy on a slide rule over more accurate but complex functions; these approximations could lead to inaccuracies and mistakes. On the other hand, the spatial, manual operation of slide rules cultivates in the user an intuition for numerical relationships and scale that people who have used only digital calculators often lack. A slide rule will also display all the terms of a calculation along with the result, thus eliminating uncertainty about what calculation was actually performed. It has thus been compared with
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does prevent scratching of the face and cursors. The highest accuracy scales are placed on the outer rings. Rather than "split" scales, high-end circular rules use spiral scales for more complex operations like log-of-log scales. One eight-inch premium circular rule had a 50-inch spiral log-log scale. Around 1970, an inexpensive model from B. C. Boykin (Model 510) featured 20 scales, including 50-inch C-D (multiplication) and log scales. The RotaRule featured a friction brake for the cursor.
772:
2365:). For example, a 10 cm (3.9 in) circular would have a maximum precision approximately equal to a 31.4 cm (12.4 in) ordinary slide rule. Circular slide rules also eliminate "off-scale" calculations, because the scales were designed to "wrap around"; they never have to be reoriented when results are near 1.0—the rule is always on scale. However, for non-cyclical non-spiral scales such as S, T, and LL's, the scale width is narrowed to make room for end margins.
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2765:, who was fortunate both in having his rule made by a firm of national reputation, and its adoption by the French Artillery. Mannheim's rule had two major modifications that made it easier to use than previous general-purpose slide rules. Such rules had four basic scales, A, B, C, and D, and D was the only single-decade logarithmic scale; C had two decades, like A and B. Most operations were done on the A and B scales; D was only used for finding squares and square roots.
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4553:. Yes, the occasional grocery store manager figured discounts on a slipstick, and this author once caught his high school English teacher calculating stats for trifecta horse-race winners on a slide rule during study hall. But slide rules never made it into daily life because you could not do simple addition and subtraction with them, not to mention the difficulty of keeping track of the decimal point. Slide rules remained tools for techies."
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1140:) rather than from unity; these are convenient in two cases. First when the user guesses a product will be close to 10 and is not sure whether it will be slightly less or slightly more than 10, the folded scales avoid the possibility of going off the scale. Second, by making the start π rather than the square root of 10, multiplying or dividing by π (as is common in science and engineering formulas) is simplified.
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310:, where each decade corresponds to a range of numbers that spans a ratio of 10 (i.e. a range from 10 to 10). For example, the range 1 to 10 is a single decade, and the range from 10 to 100 is another decade. Thus, single-decade scales (named C and D) range from 1 to 10 across the entire length of the slide rule, while double-decade scales (named A and B) range from 1 to 100 over the length of the slide rule.
1609:, for example, locate x on the D scale and read its square on the A scale. Inverting this process allows square roots to be found, and similarly for the powers 3, 1/3, 2/3, and 3/2. Care must be taken when the base, x, is found in more than one place on its scale. For instance, there are two nines on the A scale; to find the square root of nine, use the first one; the second one gives the square root of 90.
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2648:. Painted or imprinted slide rules were viewed as inferior, because the markings could wear off or be chemically damaged. Nevertheless, Pickett, an American slide rule company, made only printed scale rules. Premium slide rules included clever mechanical catches so the rule would not fall apart by accident, and bumpers to protect the scales and cursor from rubbing on tabletops.
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square roots as part of a larger calculation. Mannheim's rule also had a cursor, unlike almost all preceding rules, so any of the scales could be easily and accurately compared across the rule width. The "Mannheim rule" became the standard slide rule arrangement for the later 19th century and remained a common standard throughout the slide-rule era.
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example, instead of reading from an A scale to a D scale to find a square root, it may be possible to read from a D scale to an R1 scale running from 1 to square root of 10 or to an R2 scale running from square root of 10 to 10, where having more subdivisions marked can result in being able to read an answer with one more significant digit.
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Circular slide rules are mechanically more rugged and smoother-moving, but their scale alignment precision is sensitive to the centering of a central pivot; a minute 0.1 mm (0.0039 in) off-centre of the pivot can result in a 0.2 mm (0.0079 in) worst case alignment error. The pivot
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The width of the slide rule is quoted in terms of the nominal width of the scales. Scales on the most common "10-inch" models are actually 25 cm, as they were made to metric standards, though some rules offer slightly extended scales to simplify manipulation when a result overflows. Pocket rules
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The LLN scales can be used to compute and compare the cost or return on a fixed rate loan or investment. The simplest case is for continuously compounded interest. Example: Taking D as the interest rate in percent, slide the index (the "1" at the right or left end of the scale) of C to the percent on
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Some slide rules ("duplex" models) have scales on both sides of the rule and slide strip, others on one side of the outer strips and both sides of the slide strip (which can usually be pulled out, flipped over and reinserted for convenience), still others on one side only ("simplex" rules). A sliding
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introduced its own brand of straight slide rules, described as "faithful replica" that were "individually hand tooled". These were no longer available in 2012. In addition, Faber-Castell had a number of slide rules in inventory, available for international purchase through their web store, until mid
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When performing a sequence of multiplications or divisions by the same number, the answer can often be determined by merely glancing at the slide rule without any manipulation. This can be especially useful when calculating percentages (e.g. for test scores) or when comparing prices (e.g. in dollars
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In 1881, the
American inventor Edwin Thacher introduced his cylindrical rule, which had a much longer scale than standard linear rules and thus could calculate to higher precision, about four to five significant digits. However, the Thacher rule was quite expensive, as well as being non-portable, so
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For angles from around 5.7 up to 90 degrees, sines are found by comparing the S scale with C (or D) scale. (On many closed-body rules the S scale relates to the A and B scales instead and covers angles from around 0.57 up to 90 degrees; what follows must be adjusted appropriately.) The S scale has a
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For example, setting 7.5 on one scale over 10 on the other scale, the user can see that at the same time 1.5 is over 2, 2.25 is over 3, 3 is over 4, 3.75 is over 6, 4.5 is over 6, and 6 is over 8, among other pairs. For a real-life situation where 750 represents a whole 100%, these readings could be
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are still used though no longer on a routine basis. These rules are used as part of the teaching and instruction process as in learning to use them the student also learns about the principles behind the calculations, it also allows the student to be able to use these instruments as a backup in the
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are damaged or have missing parts, and the seller may not know enough to supply the relevant information. Replacement parts are scarce, expensive, and generally available only for separate purchase on individual collectors' web sites. The
Keuffel and Esser rules from the period up to about 1950 are
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Some engineering students and engineers carried ten-inch slide rules in belt holsters, a common sight on campuses even into the mid-1970s. Until the advent of the pocket digital calculator, students also might keep a ten- or twenty-inch rule for precision work at home or the office while carrying a
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for two or three months. The simultaneous equation contained up to seven unknown quantities, took about a week to solve, and had to be repeated with a different selection of slack wires if the guess on which of the eight radial wires were slack was wrong and one of the wires guessed to be slack was
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Circular slide rules come in two basic types, one with two cursors, and another with a free dish and one cursor. The dual cursor versions perform multiplication and division by holding a constant angle between the cursors as they are rotated around the dial. The onefold cursor version operates more
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Base-10 logarithms and exponentials are found using the L scale, which is linear. Some slide rules have a Ln scale, which is for base e. Logarithms to any other base can be calculated by reversing the procedure for calculating powers of a number. For example, log2 values can be determined by lining
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As with mainframe computing, the availability of these desktop machines did not significantly affect the ubiquitous use of the slide rule, until cheap hand-held scientific electronic calculators became available in the mid-1970s, at which point it rapidly declined. The pocket-sized
Hewlett-Packard
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Mannheim changed the C scale to a single-decade scale and performed most operations with C and D instead of A and B. Because the C and D scales were single-decade, they could be read more precisely, so the rule's results could be more accurate. The change also made it easier to include squares and
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Slide rules have often been specialized to varying degrees for their field of use, such as excise, proof calculation, engineering, navigation, etc., and some slide rules are extremely specialized for very narrow applications. For example, the John Rabone & Sons 1892 catalog lists a "Measuring
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The main disadvantages of circular slide rules are the difficulty in locating figures along a dish, and limited number of scales. Another drawback of circular slide rules is that less-important scales are closer to the center, and have lower precisions. Most students learned slide rule use on the
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To extract a cube root using a slide rule with only C/D and A/B scales, align 1 on the B cursor with the base number on the A scale (taking care as always to distinguish between the lower and upper halves of the A scale). Slide the slide until the number on the D scale which is against 1 on the C
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Slide rules exist in a diverse range of styles and generally appear in a linear, circular or cylindrical form. Slide rules manufactured for specialized fields such as aviation or finance typically feature additional scales that aid in specialized calculations particular to those fields. The slide
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At least one circular rule, a 1931 Gilson model, sacrificed some of the scales usually found in slide rules in order to obtain additional resolution in multiplication and division. It functioned through the use of a spiral C scale, which was claimed to be 50 feet and readable to five significant
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second set of angles (sometimes in a different color), which run in the opposite direction, and are used for cosines. Tangents are found by comparing the T scale with the C (or D) scale for angles less than 45 degrees. For angles greater than 45 degrees the CI scale is used. Common forms such as
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Even during their heyday, slide rules never caught on with the general public. Addition and subtraction are not well-supported operations on slide rules and doing a calculation on a slide rule tends to be slower than on a calculator. This led engineers to use mathematical equations that favored
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circular slide rule used by pilots has been in continuous production and remains available in a variety of models. Some wrist watches designed for aviation use still feature slide rule scales to permit quick calculations. The
Citizen Skyhawk AT and the Seiko Flightmaster SNA411 are two notable
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Various other conveniences have been developed. Trigonometric scales are sometimes dual-labeled, in black and red, with complementary angles, the so-called "Darmstadt" style. Duplex slide rules often duplicate some of the scales on the back. Scales are often "split" to get higher accuracy. For
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Many sailors keep slide rules as backups for navigation in case of electric failure or battery depletion on long route segments. Slide rules are still commonly used in aviation, particularly for smaller planes. They are being replaced only by integrated, special purpose and expensive flight
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has reduced the use of dead reckoning for aerial navigation, and handheld calculators have taken over many of its functions, the E6B remains widely used as a primary or backup device and the majority of flight schools demand that their students have some degree of proficiency in its use.
2384:. With the aid of scales printed on the frame it also helps with such miscellaneous tasks as converting time, distance, speed, and temperature values, compass errors, and calculating fuel use. The so-called "prayer wheel" is still available in flight shops, and remains widely used. While
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and square it using the A and B scales as described above. Alternatively, use the rightmost 1 on the C scale, and read the answer off the next higher LL scale. For example, aligning the rightmost 1 on the C scale with 2 on the LL2 scale, 3 on the C scale lines up with 8 on the LL3 scale.
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Specialized slide rules were invented for various forms of engineering, business and banking. These often had common calculations directly expressed as special scales, for example loan calculations, optimal purchase quantities, or particular engineering equations. For example, the
2345:, and the user estimates the third figure. Some high-end slide rules have magnifier cursors that make the markings easier to see. Such cursors can effectively double the accuracy of readings, permitting a 10-inch slide rule to serve as well as a 20-inch model.
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with a vertical alignment line is used to find corresponding points on scales that are not adjacent to each other or, in duplex models, are on the other side of the rule. The cursor can also record an intermediate result on any of the scales.
3126:). This separate calculation forces the user to keep track of magnitude in short-term memory (which is error-prone), keep notes (which is cumbersome) or reason about it in every step (which distracts from the other calculation requirements).
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There are still a handful of sources for brand new slide rules. The
Concise Company of Tokyo, which began as a manufacturer of circular slide rules in July 1954, continues to make and sell them today. In September 2009, on-line retailer
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invented the log log slide rule, which included a scale displaying the logarithm of the logarithm. This allowed the user to directly perform calculations involving roots and exponents. This was especially useful for fractional powers.
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from position on the ruler as each function's input. Calculations that can be reduced to simple addition or subtraction using those precomputed functions can be solved by aligning the two rulers and reading the approximate result.
2626:-clad bamboo, which had the advantages of being dimensionally stable, strong, and naturally self-lubricating. These bamboo slide rules were introduced in Sweden in September, 1933, and probably only a little earlier in Germany.
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Because pairs of numbers that are aligned on the logarithmic scales form constant ratios, no matter how the scales are offset, slide rules can be used to generate equivalent fractions that solve proportion and percent problems.
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Astronomical work also required precise computations, and, in 19th-century
Germany, a steel slide rule about two meters long was used at one observatory. It had a microscope attached, giving it accuracy to six decimal places.
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is claimed to be " most extensive resource for all things concerning slide rules and logarithmic calculators". The museum's Web page includes extensive literature relative to slide rules in its "Slide Rule
Library" section.
3050:(coordinate rotation digital computer) algorithm, which allows for calculation of trigonometric functions using only shift and add operations. This method facilitated the development of ever smaller scientific calculators.
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profession during the later 19th century drove widespread slide-rule use, beginning in Europe and eventually taking hold in the United States as well. The duplex rule was invented by
William Cox in 1891 and was produced by
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Around 1974, lower-cost handheld electronic scientific calculators started to make slide rules largely obsolete. By 1975, basic four-function electronic calculators could be purchased for less than $ 50, and by 1976 the
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D. The corresponding value on LL2 directly below the index will be the multiplier for 10 cycles of interest (typically years). The value on LL2 below 2 on the C scale will be the multiplier after 20 cycles, and so on.
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This slide rule is positioned to yield several values: From C scale to D scale (multiply by 2), from D scale to C scale (divide by 2), A and B scales (multiply and divide by 4), A and D scales (squares and square
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Even in the 21st century, some people prefer a slide rule over an electronic calculator as a practical computing device. Others keep their old slide rules out of a sense of nostalgia, or collect them as a hobby.
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A Department of
Defense publication from 1962 infamously included a special-purpose circular slide rule for calculating blast effects, overpressure, and radiation exposure from a given yield of an atomic bomb.
2555:, and those with bars, such as the Thacher and some Loga models. In either case, the advantage is a much longer scale, and hence potentially greater precision, than afforded by a straight or circular rule.
2396:. Lining up the original and desired size values on the inner and outer wheels will display their ratio as a percentage in a small window. Though not as common since the advent of computerized layout, they
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Many slide rules have S, T, and ST scales marked with degrees and minutes (e.g. some
Keuffel and Esser models (Doric duplex 5" models, for example), late-model Teledyne-Post Mannheim-type rules). So-called
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up either leftmost or rightmost 1 on the C scale with 2 on the LL2 scale, finding the number whose logarithm is to be calculated on the corresponding LL scale, and reading the log2 value on the C scale.
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calculations can be performed hands-free at a glance with a slide rule. Other useful linear conversions such as pounds to kilograms can be easily marked on the rule and used directly in calculations.
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With more complex calculations involving multiple factors in the numerator and denominator of an expression, movement of the scales can be minimized by alternating divisions and multiplications. Thus
106:, the slide rule is not meant to be used for measuring length or drawing straight lines. Nor is it designed for addition or subtraction, which is usually performed using other methods, like using an
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In 1722, Warner introduced the two- and three-decade scales, and in 1755 Everard included an inverted scale; a slide rule containing all of these scales is usually known as a "polyphase" rule.
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1974:. For angles below 5.7 degrees, sines, tangents, and radians are approximately equal, and are found on the ST or SRT (sines, radians, and tangents) scale, or simply divided by 57.3 degrees/
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scientific calculator was the first handheld device of its type, but it cost US$ 395 in 1972. This was justifiable for some engineering professionals, but too expensive for most students.
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The importance of the slide rule began to diminish as electronic computers, a new but rare resource in the 1950s, became more widely available to technical workers during the 1960s.
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There is more than one method for doing division, and the method presented here has the advantage that the final result cannot be off-scale, because one has a choice of using the
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is used to track the decimal point for more precise calculations. Addition and subtraction steps in a calculation are generally done mentally or on paper, not on the slide rule.
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2144:{\displaystyle {\begin{aligned}\left({\frac {x}{y}}+1\right)y&=x+y\,{\text{ (addition)}},\\\left({\frac {x}{y}}-1\right)y&=x-y\,{\text{ (subtraction)}}.\end{aligned}}}
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Pilot balloon slide rules were used by meteorologists in weather services to determine the upper wind velocities from an ascending hydrogen or helium-filled pilot balloon.
2881:, an algorithm for rapidly computing products that predates logarithms. However, there has been little practical interest in constructing one beyond the initial prototype.
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Traditionally slide rules were made out of hard wood such as mahogany or boxwood with cursors of glass and metal. At least one high precision instrument was made of steel.
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scales, single sections of the same length, used together for multiplication and division, and generally one of them is combined with another scale for other calculations
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to use slide rules. The UIL had been originally been organized in 1910 to administer literary events, but had become the governing body of school sports events as well.
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marked with powers of 2, calculating 8x4 by aligning the bottom ruler to start where the top ruler is 8, and then reading at the number above where the bottom ruler is 4.
1087:. On linear rules, the scales and their labeling are highly standardized, with variation usually occurring only in terms of which scales are included and in what order.
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a "sliding rule" that contained scaled trigonometric functions on the fixed part and a line of log-sines and log-tans on the slider used to solve navigation problems.
3137:, compared to many digits on digital calculators. As order of magnitude gets the greatest prominence when using a slide rule, users are less likely to make errors of
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on the top is moved to a factor on the bottom, and the answer is read off the bottom where the other factor is on the top. This works because the distances from the
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While the above example lies within one decade, users must mentally account for additional zeroes when dealing with multiple decades. For example, the answer to
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of Oxford developed a calculating device with a single logarithmic scale; with additional measuring tools it could be used to multiply and divide. In c. 1622,
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is found by first positioning the top scale to start above the 2 of the bottom scale, and then reading the marking 1.4 off the bottom two-decade scale where
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A simple circular slide rule, made by Concise Co., Ltd., Tokyo, Japan, with only inverse, square, and cubic scales. On the reverse is a handy list of 38
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cursor is the same as the number on the B cursor which is against the base number on the A scale. (Examples: A 8, B 2, C 1, D 2; A 27, B 3, C 1, D 3.)
3352:, was donated to MIT around 2005, substantially expanding existing holdings. Selected items from the collection are usually on display at the museum.
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company distributed a customized slide rule adapted to solving the equations used for selecting the proper size of industrial flow control valves.
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The first step away from slide rules was the introduction of relatively inexpensive electronic desktop scientific calculators. These included the
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145:. The slide rule's ease of use, ready availability, and low cost caused its use to continue to grow through the 1950s and 1960s, even as desktop
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Although a great many slide rules are circulating on the market, specimens in good condition tend to be expensive. Many rules found for sale on
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Then in the early 1970s the first electronic hand-held calculators appeared on the market, and within ten years the slide rule was obsolete.
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are typically 5 inches (12 cm). Models a couple of metres (yards) wide were made to be hung in classrooms for teaching purposes.
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and the prior claims of Wingate. Oughtred's ideas were only made public in publications of his student William Forster in 1632 and 1653.
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A Russian circular slide rule built like a pocket watch that works as single cursor slide rule since the two needles are ganged together
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of the answer to position the decimal point in the results. For example, 1.5 × 30 (which equals 45) will show the same result as
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on the D scale. The cursor is then moved along the rule until a position is found where the numbers on the CI and D scales add up to
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scale, three sections each of which is one third the length of the C and D scales, used for finding cube roots and cubes of numbers
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The basic advantage of a circular slide rule is that the widest dimension of the tool was reduced by a factor of about 3 (i.e. by
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Addition and subtraction aren't typically performed on slide rules, but is possible using either of the following two techniques:
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scales, two sections each of which is half the length of the C and D scales, used for finding square roots and squares of numbers
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3265:) variant. Another prized American model is the eight-inch (20 cm) Scientific Instruments circular rule. Of European rules,
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4060:"Lot 25368 Buzz Aldrin's Apollo 11 Slide Rule – Flown to the Moon. ... 2007 September Grand Format Air & Space Auction #669"
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or batteries. Mechanical imprecision in slide rules that were poorly constructed or warped by heat or use will lead to errors.
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sheets with calculations "the truth stood revealed (and) produced a satisfaction almost amounting to a religious experience".
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After sliding the cursor right (for addition) or left (for subtraction) and returning the slide to 0, the result can be read.
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Pickett circular slide rule with two cursors. (4.25 in/10.9 cm width) Reverse has additional scale and one cursor.
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scales, for working with logarithms of any base and arbitrary exponents. 4, 6, or 8 scales of this type are commonly seen.
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The Binary Slide Rule manufactured by Gilson in 1931 performed an addition and subtraction function limited to fractions.
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In 1845, Paul Cameron of Glasgow introduced a nautical slide rule capable of answering navigation questions, including
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to make a device that is recognizably the modern slide rule. Oughtred became involved in a vitriolic controversy over
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3042:, introduced in 1968. Both of these were programmable and provided exponential and logarithmic functions; the HP had
2196:, other calculations can also be made with one movement. For example, reciprocal scales can be used for the equality
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used for addition, subtraction, and (along with the C and D scales) for finding base-10 logarithms and powers of 10
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Slide – a center strip interlocked with the frame that can move lengthwise relative to the frame.
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It is believed they may still have some slide rules, but their new website and online store does not carry them.
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Then, just a decade ago, the invention of the pocket calculator made the slide rule obsolete almost overnight...
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Wang Laboratories (December 1966). "Now you can determine Copolymer Composition in a few minutes at your desk".
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introduced a pilot's wristwatch with an integrated circular slide rule specialized for flight calculations: the
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Throughout the 1950s and 1960s, the slide rule was the symbol of the engineer's profession in the same way the
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Scales were also made of celluloid or other polymers, or printed on aluminium. Later cursors were molded from
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In 2004, education researchers David B. Sher and Dean C. Nataro conceived a new type of slide rule based on
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The S, T, and ST scales are used for trig functions and multiples of trig functions, for angles in degrees.
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With two logarithmic scales, the act of positioning the top scale to start at the bottom scale's label for
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that the quotient of two variables plus (or minus) one times the divisor equals their sum (or difference):
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3423: – hand-held device with moving parts, commonly paper, commonly printed for reference or calculation
3443: – Paper construct with rotating parts, may be considered a subclass of slide chart or movable book
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interpreted to suggest that 150 is 20%, 225 is 30%, 300 is 40%, 375 is 50%, 450 is 60%, and 600 is 80%.
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Runner or glass – an exterior sliding piece with a hairline, also known as the "cursor".
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ruler can be aligned with the start of another such ruler to sum their logarithms. Then by applying the
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4124:"The Prosthaphaeretic Slide Rule: A Mechanical Multiplication Device Based On Trigonometric Identities"
3257:, a premium scientific and engineering slide rule available both in a ten-inch (25 cm) "regular" (
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2153:
This is similar to the addition/subtraction technique used for high-speed electronic circuits with a
1582:
There are single-decade (C and D), double-decade (A and B), and triple-decade (K) scales. To compute
1084:
1076:
600:
237:
3301:
Various slide rule simulator apps are available for Android and iOS-based smart phones and tablets.
2644:
All premium slide rules had numbers and scales deeply engraved, and then filled with paint or other
2418:/time of climb/descent, flight time, distance, and fuel consumption functions, as well as kilometer—
125:
and others developed the slide rule in the 17th century based on the emerging work on logarithms by
110:. Maximum accuracy for standard linear slide rules is about three decimal significant digits, while
5084:
4063:
3408:
3349:
3235:
2696:
2491:
2407:
2342:
1709:
1703:
1528:
771:
327:
transform the operations of multiplication and division to addition and subtraction, respectively:
256:
232:
of the two numbers can be read. More elaborate slide rules can perform other calculations, such as
111:
4970:
1760:
4391:
4235:
4033:
3728:
3699:
3153:
3146:
3134:
3106:
2725:
2552:
2193:
2007:
Converting addition and subtraction to division (required for the C and D or comparable scales):
1231:
307:
197:
115:
5041:
4999:
3251:
2814:
from 1924. The stress calculations for each transverse frame required computations by a pair of
2329:
102:
used for application-specific computations. Though similar in name and appearance to a standard
4399:
3085:
2753:
993:
in the top scale in the figure above, without the need to register the intermediate result for
724:
279:
Frame or base – two strips of the same length held parallel with a gap between.
4519:
4478:
4450:
4383:
4227:
4041:
4025:
3978:
3874:
3837:
3831:
3687:
3588:
3563:
3504:
3498:
3468:
3345:
3032:
2831:
2692:
2544:
2319:
1565:
1072:
221:
2410:. The Navitimer circular rule, referred to by Breitling as a "navigation computer", featured
1940:
1658:
568:
516:
4501:
4375:
4320:
4219:
4017:
3970:
3414:
3046:(sine, cosine, and tangent) and hyperbolic trigonometric functions as well. The HP used the
2877:
2717:
2700:
2688:
2660:
2380:. This is a circular slide rule first created in the 1930s for aircraft pilots to help with
1808:
1368:
1261:
1064:
1033:
303:
193:
122:
60:
39:
3035:
LOCI-2, introduced in 1965, which used logarithms for multiplication and division; and the
2543:
There are two main types of cylindrical slide rules: those with helical scales such as the
1845:
1615:
1585:
1456:
1398:
5015:
4974:
4515:
3796:
3781:
3668:
3533:
3396:
3381:
3304:
Specialized slide rules such as the E6B used in aviation, and gunnery slide rules used in
3138:
3036:
2910:
2738:
91:
3774:
2706:
In 1677, Henry Coggeshall created a two-foot folding rule for timber measure, called the
4013:
3870:
3789:
3713:
3378: – Person performing mathematical calculations, before calculators became available
2893:
There were many specialized slide rules for photographic applications. For example, the
2890:
Tape and Cattle Gauge", a device to estimate the weight of a cow from its measurements.
1545:
3387:
2849:
2757:
Engineer using a slide rule, with mechanical calculator in background, mid 20th century
2439:
2381:
1899:
1879:
1552:
1436:
1267:
1211:
548:
496:
67:
4530:
The first hand calculator appeared in 1972 and made the slide rule obsolete overnight.
4021:
2392:
Proportion wheels are simple circular slide rules used in graphic design to calculate
5063:
4509:
4428:
3434:
3266:
3239:
2684:
2634:
2630:
2435:
2419:
2415:
2254:
1643:
on it. First, align the leftmost 1 on the C scale with x on the LL scale. Then, find
165:
4991:
4812:
4239:
2761:
A more modern form of slide rule was created in 1859 by French artillery lieutenant
4505:
4293:
3093:
explicitly comparing electronic computers to engineers calculating with slide rules
2403:
2393:
2158:
1970:
on the S scale to the result on the D scale, when the C scale index is set at
935:
252:
209:
87:
17:
4961:
4644:"Citizen Watch Company – Citizen Eco-Drive / US, Canada, UK, IrelandCitizen Watch"
4395:
4339:
3647:
3066:
scientific calculator was sold for less than $ 25 ($ 134 adjusted for inflation).
2667:
1639:
problems, use the LL scales. When several LL scales are present, use the one with
1038:
251:
The user may estimate the location of the decimal point in the result by mentally
4549:. "The difficulty of learning to use slide rules discouraged their use among the
4223:
3462:
4932:
4888:
4210:
Ross, M. G. (2003). "Circle of time: errors in the use of the pregnancy wheel".
3420:
3286:
2974:
2894:
2853:
2842:
2793:
2773:
2742:
2676:
1047:
In addition to the logarithmic scales, some slide rules have other mathematical
267:
233:
201:
185:
142:
130:
126:
4765:
4740:
4253:
2184:
4715:
4550:
4489:
With the invention of the calculator the slide rule became instantly obsolete.
4379:
3809:
3329:
3322:
3305:
2824:
2358:
like the standard slide rule through the appropriate alignment of the scales.
43:
Typical ten-inch (25 cm) student slide rule (Pickett N902-T simplex trig)
4387:
4029:
3982:
3727:
Istvan, Szalkai (2016). "General Two-variable Functions on the Slide-rule".
3294:
3278:
2926:
Circular slide rules to estimate ovulation dates and fertility are known as
2861:
2857:
2680:
2623:
2548:
241:
83:
75:
5029:
4672:
4231:
4045:
3560:
American Thesaurus of Slang: A Complete Reference Book of Colloquial Speech
3437: – Auxiliary scale of a measurement device, used to increase precision
1531:
and (2) to accurately determine cosine for small angles (with the S scale)
3788:. An instruction manual for the unit marketed by Dietzgen can be found at
3567:
2333:
A 7-foot (2.1 m) teaching slide rule compared to a normal-sized model
3752:
3440:
3402:
3348:
Company collection, from the slide rule manufacturer formerly located in
3337:
3277:
particularly problematic, because the end-pieces on the cursors, made of
3039:
2411:
755:
for example, by positioning the top scale to start at the bottom scale's
158:
99:
79:
4324:
4189:
4128:
Mathematics And Computer Education, Vol. 38, Iss. 1 (Winter 2004): 37–43
4037:
3997:
291:
5047:
4998:
4826:
3090:
2835:
2811:
2785:
it was used in far more limited numbers than conventional slide rules.
5014:
4160:
3974:
3615:
3584:
An Engineer's Alphabet: Gleanings from the Softer Side of a Profession
3289:
may be used to recreate missing or irretrievably broken cursor parts.
3016:
1978:. Inverse trigonometric functions are found by reversing the process.
4273:
3785:
3369:
3285:
may be used to slow the deterioration of some older slide rules, and
3047:
2988:
Cryptographic slide rule used by the Swiss Army between 1914 and 1940
1975:
107:
3863:
Encyclopedia of the Scientific Revolution: From Copernicus to Newton
3207:. Statements consisting only of original research should be removed.
2901:
was a two-slide boxwood, brass, and cardboard device for estimating
2656:
157:
and became inexpensive in the mid-1970s, slide rules became largely
4693:
3733:
3704:
513:
corresponds to shifting the top logarithmic scale by a distance of
4956:
3316:
3234:
3084:
3074:
3063:
3055:
3021:
3015:
2752:
2666:
2655:
2645:
2622:
In 1895, a Japanese firm, Hemmi, started to make slide rules from
2328:
2183:
1037:
266:
179:
154:
134:
103:
63:
1876:), and then aligning the index ("1") of the C scale to the value
4985:
2807:
1056:
141:, it was the most commonly used calculation tool in science and
52:
3485:
The slide rule is an example of a mechanical analog computer...
3411: – Mathematical instrument consisting of two hinged rulers
721:, the mark on the bottom scale at that position corresponds to
5038:— French Slide Rules (Graphoplex, Tavernier-Gravet and others)
3172:
3161:
2920:
2860:
was sold at auction in 2007. The model N600-ES taken along on
2710:, expanding the slide rule's use beyond mathematical inquiry.
2377:
2376:
One slide rule remaining in daily use around the world is the
889:
mark are proportional to the logarithms of the marked values.
1433:
used along with the C and D scales for finding natural (base
2675:
The slide rule was invented around 1620–1630, shortly after
2242:{\displaystyle {\frac {1}{x}}+{\frac {1}{y}}={\frac {1}{z}}}
4979:
4087:. Smithsonian National Air and Space Museum. Archived from
3152:
Being entirely mechanical, a slide rule does not depend on
2362:
2341:
Typically the divisions mark a scale to a precision of two
1137:
763:
can then be read on the bottom scale under the top scale's
4982:— Dedicated to the preservation and history of slide rules
3907:
Kells, Lyman M.; Kern, Willis F.; Bland, James R. (1943).
3298:
2018. Proportion wheels are still used in graphic design.
3269:'s high-end models are the most popular among collectors.
3024:
scientific calculator, introduced for under US$ 25 in 1976
4962:
The history, theory and use of the engineering slide rule
4564:"Problem-based learning and the three C's of technology,"
3910:
The Log-Log Duplex Decitrig Slide Rule No. 4081: A Manual
3105:
A slide rule requires the user to separately compute the
1757:
can be solved by first reducing the equation to the form
1071:) (for taking the log of a value on a multiplier scale),
3521:
For example, slide rules are mechanical analog computers
2923:
is a circular slide rule used by pilots and navigators.
2823:
not slack. After months of labour filling perhaps fifty
1051:
encoded on other auxiliary scales. The most popular are
4988:– Comprehensive Aristo site with many search facilities
4967:
4858:. Massachusetts Institute of Technology. Archived from
3928:
The Polyphase Duplex Slide Rule, A Self-Teaching Manual
3392:
Pages displaying short descriptions of redirect targets
3309:
event that the modern electronics in general use fail.
3196:
2373:
linear slide rules, and did not find reason to switch.
897:
The illustration below demonstrates the computation of
3810:"336 (Teknisk Tidskrift / 1933. Allmänna avdelningen)"
3775:
http://www.sphere.bc.ca/test/gilson/gilson-manual2.jpg
4673:"Greg's Slide Rules – Links to Slide Rule Collectors"
4511:
Beyond calculation: the next fifty years of computing
3790:
http://www.sliderulemuseum.com/SR_Library_General.htm
2263:
2202:
2020:
1943:
1902:
1882:
1848:
1811:
1763:
1712:
1661:
1618:
1588:
1496:
1459:
1439:
1401:
1371:
1270:
1234:
1214:
822:
For an example with even larger numbers, to multiply
727:
653:
603:
571:
551:
519:
499:
412:
335:
5054:
Descriptions, alphabetical by brandname, with images
3425:
Pages displaying wikidata descriptions as a fallback
3160:
computers, and not general-purpose calculators. The
2848:
Aluminium Pickett-brand slide rules were carried on
1151:
scales running from right to left, used to simplify
826:, the top scale is again positioned to start at the
4833:. Massachusetts Institute of Technology. 2005-01-11
2422:and gallon—liter fuel amount conversion functions.
2257:, etc.), and quadratic scales can be used to solve
2170:Using a linear L scale (available on some models):
4994:— Javascript simulations of historical slide rules
4909:Turner, Kimberli (2009-10-07). "Slide Rule: 101".
3688:"General Two-Variable Functions on the Slide Rule"
2834:designed and constructed a circular slide rule in
2302:
2241:
2143:
1958:
1916:. These two values are the roots of the equation.
1908:
1888:
1868:
1834:
1797:
1749:
1682:
1631:
1601:
1519:
1472:
1445:
1414:
1387:
1276:
1252:
1220:
739:
713:
639:
589:
557:
537:
505:
478:
400:{\displaystyle \log(x\times y)=\log(x)+\log(y)\,,}
399:
149:were gradually introduced. But after the handheld
3913:. Keuffel & Esser. p. 92. Archived from
1986:models use decimal fractions of degrees instead.
4085:"Slide Rule, 5-inch, Pickett N600-ES, Apollo 13"
3558:Berrey, Lester V.; van den Bark, Melvin (1953).
3497:Ernst Bleuler; Robert Ozias Haxby (2011-09-21).
1647:on the C scale and go down to the LL scale with
1083:) scales. Others feature scales for calculating
858:, the answer must additionally be multiplied by
5050:— Information from The Museum of HP Calculators
4694:"Restoring and Repairing Slide Rules and Notes"
4212:Journal of Maternal-Fetal and Neonatal Medicine
3390: – Computer approximation for real numbers
3336:, has a collection of hundreds of slide rules,
1651:on it. That scale will indicate the answer. If
1132:versions of the C and D scales that start from
714:{\displaystyle \log(x)+\log(y)=\log(x\times y)}
66:for evaluating mathematical operations such as
4964:— By Dr James B. Calvert, University of Denver
4122:Sher, David B.; Nataro, Dean C. (2009-06-02).
3895:The Practical Mechanic and Engineer's Magazine
3616:"Eric's Types of Slide Rules and their Scales"
3587:. Cambridge University Press. pp. 46–47.
3321:A classroom-sized slide rule displayed at the
2905:from time of day, time of year, and latitude.
2872:five-inch pocket slide rule around with them.
2157:in specialized computer applications like the
838:, all numbers in that scale are multiplied by
811:. Thus, even though the answer directly reads
220:For example, a number to be multiplied on one
4423:Behrens, Lawrence; Rosen, Leonard J. (1982).
4340:"The HP 9100 Project: An Exothermic Reaction"
3102:(RPN) implemented in electronic calculators.
3012:History of computing hardware (1960s–present)
2507:The front side of a Boykin RotaRule Model 510
923:on the bottom scale. The resulting quotient,
121:English mathematician and clergyman Reverend
8:
4813:"Commons category MIT Slide Rule Collection"
3946:. London: William Heinemann. pp. 76–78.
3384: – Circular slide rule used in aviation
3089:December 1951 advertisement for the IBM 604
3081:Comparison to electronic digital calculators
2519:The rear side of a Boykin RotaRule Model 510
479:{\displaystyle \log(x/y)=\log(x)-\log(y)\,.}
3281:, tend to chemically break down over time.
2852:space missions. The model N600-ES owned by
597:with the bottom scale's number at position
161:, so most suppliers departed the business.
4968:United Kingdom Slide Rule Circle Home Page
4449:. Princeton University Press. p. 16.
3751:. Tbullock.com. 2009-12-08. Archived from
168:, the slide rule is colloquially called a
4425:Writing and reading across the curriculum
4112:, American Technical Society, 1961, p. 5.
3732:
3703:
3223:Learn how and when to remove this message
2294:
2281:
2268:
2262:
2229:
2216:
2203:
2201:
2129:
2128:
2088:
2071:
2070:
2030:
2021:
2019:
1942:
1901:
1881:
1858:
1847:
1824:
1810:
1768:
1762:
1720:
1711:
1670:
1666:
1660:
1623:
1617:
1593:
1587:
1509:
1497:
1495:
1464:
1458:
1438:
1406:
1400:
1376:
1370:
1269:
1244:
1235:
1233:
1213:
927:, can then be read below the top scale's
726:
652:
602:
570:
550:
518:
498:
472:
425:
411:
393:
334:
275:Most slide rules consist of three parts:
4595:Stoll, Cliff. "When Slide Rules Ruled",
4578:Stoll, Cliff. "When Slide Rules Ruled,"
4541:Stoll, Cliff. "When Slide Rules Ruled,"
2958:John Rabone & Sons 1892 cattle gauge
2792:In the 1920s, the novelist and engineer
2466:A two-scale slide rule built into a ring
1089:
38:
3540:. Massachusetts Institute of Technology
3467:. Vol. 1. Macmillan. p. 175.
3453:
2936:
2663:(1575–1660), inventor of the slide rule
2557:
2424:
129:. It made calculations faster and less
1564:The scales on the front and back of a
545:. This aligns each top scale's number
5032:— A very big Faber Castell collection
4980:Oughtred Society Slide Rule Home Page
4615:"In Praise Of RPN (with Python Or C)"
2679:'s publication of the concept of the
1197:on the C and CI (or D and DI) scales
7:
3836:. Courier Corporation. p. 205.
919:on the top scale is placed over the
4675:. Sliderule.ozmanor.com. 2004-07-29
4567:The Power of Problem-Based Learning
4062:. Heritage Auctions. Archived from
3897:, April 1845, p. 187 and Plate XX-B
3405: – Analog graphical calculator
3399: – American computer scientist
3250:A popular collectible model is the
2845:is that of the medical profession.
2691:of Cambridge combined two handheld
2495:wristwatch with circular slide rule
1284:) under the cursor on the DF scale
759:, the result of the multiplication
4992:Derek's virtual slide rule gallery
3786:http://www.hpmuseum.org/srcirc.htm
2856:that flew with him to the Moon on
1208:– setting the cursor to any value
25:
5080:Historical scientific instruments
4475:Inventions that Changed the World
4368:Journal of VLSI Signal Processing
4022:10.1038/scientificamerican0506-80
3893:"Cameron's Nautical Slide Rule",
3071:University Interscholastic League
2671:1763 illustration of a slide rule
2303:{\displaystyle x^{2}+y^{2}=z^{2}}
1520:{\displaystyle {\sqrt {1-x^{2}}}}
226:law of the logarithm of a product
4254:"The Effects of Nuclear Weapons"
3857:Applebaum, Wilbur (2003-12-16).
3177:
2993:
2981:
2963:
2951:
2939:
2820:Fuller's cylindrical slide rules
2745:of the sun and principal stars.
2596:
2584:
2572:
2560:
2524:
2512:
2500:
2483:
2471:
2459:
2447:
2427:
1551:
1544:
934:
846:set of numbers is multiplied by
788:
770:
4957:International Slide Rule Museum
4929:International Slide Rule Museum
4789:. Faber-Castell. Archived from
4714:. Concise.co.jp. Archived from
4698:International Slide Rule Museum
4625:from the original on 2023-09-23
3799:. All retrieved March 14, 2007.
3692:Journal of the Oughtred Society
3503:. Academic Press. p. 638.
3357:International Slide Rule Museum
3133:of a slide rule is about three
3069:1980 was the final year of the
2188:Quadratic and reciprocal scales
640:{\displaystyle \log(x)+\log(y)}
5006:New International Encyclopedia
4925:"Slide Rule Library Main Desk"
4887:. Proun Design. Archived from
3669:"AntiQuark: Slide Rule Tricks"
3646:. pp. 7–8. Archived from
3614:Marcotte, Ph.D., Eric (2002).
1034:Slide rule scale § Scales
708:
696:
684:
678:
666:
660:
634:
628:
616:
610:
584:
578:
532:
526:
469:
463:
451:
445:
433:
419:
390:
384:
372:
366:
354:
342:
1:
4359:Volder, Jack E. (June 2000).
4141:– via Findarticles.com.
3957:Witcher, C. M. (1954-12-01).
3417: – Mechanical calculator
3283:Methods of preserving plastic
2866:National Air and Space Museum
2806:on the design of the British
2796:(he called his autobiography
2604:
2531:Sperry 4016 Pocket Calculator
2402:In 1952, Swiss watch company
1750:{\displaystyle ax^{2}+bx+c=0}
255:between labeled graduations.
114:is used to keep track of the
4911:Colorado Hometown Newspapers
4224:10.1080/14767050412331312200
3940:Norway, Nevil Shute (1954).
3930:, Breckenridge, 1922, p. 20.
3461:Roger R. Flynn (June 2002).
3261:) and a five-inch "pocket" (
3091:Electronic Calculating Punch
2731:American Practical Navigator
2699:, with his one-time student
2192:Using (almost) any strictly
1798:{\displaystyle x^{2}-px+q=0}
1699:Roots of quadratic equations
1568:(K&E) 4181-3 slide rule
862:. The answer directly reads
854:in the top scale represents
184:Simple slide rule made from
139:scientific pocket calculator
90:. It is one of the simplest
4764:. ThinkGeek. Archived from
4739:. ThinkGeek. Archived from
4613:Williams, Al (2023-06-21).
4182:"Pilot Balloon Slide Rules"
3203:the claims made and adding
3119: × 0.03 (which equals
1990:Logarithms and exponentials
1655:is "off the scale", locate
1253:{\displaystyle {\pi }r^{2}}
830:on the bottom scale. Since
803:set of numbers that number
137:. Before the advent of the
98:rule is closely related to
32:Slide rule (disambiguation)
5121:
5036:Collection of slide rules
4881:"MIT Museum — Slide Rules"
4473:Castleden, Rodney (2007).
3009:
2317:
2161:(GRAPE) supercomputer and
1966:can be read directly from
1031:
989:, can be read beneath the
874:to get the actual answer:
842:. Thus, any answer in the
29:
27:Mechanical analog computer
3784:. A photo can be seen at
3562:(2nd ed.). Crowell.
2946:An E6-B aviation computer
2155:logarithmic number system
1097:single-decade logarithmic
740:{\displaystyle x\times y}
4986:Rod Lovett's Slide Rules
4827:"MIT Museum measures up"
4447:e: The Story of a Number
4338:Leibson, Steven (2010).
4274:"Strangelove Slide Rule"
4108:Charles Overton Harris,
3998:"When Slide Rules Ruled"
3830:Smith, David E. (1958).
3686:Istvan, Szalkai (2016).
3581:Petroski, Henry (2011).
3372: – Calculating tool
3334:Cambridge, Massachusetts
3145:per kilogram). Multiple
2864:in 1970 is owned by the
2398:are still made and used.
1999:Addition and subtraction
1119:three-decade logarithmic
815:, the correct answer is
5105:17th-century inventions
4477:. Futura. p. 157.
4380:10.1023/a:1008110704586
4298:oldcalculatormuseum.com
3959:"Physics without sight"
3100:reverse Polish notation
3044:trigonometric functions
2885:Specialized calculators
2567:Fuller calculator, 1928
2539:Cylindrical slide rules
1959:{\displaystyle k\sin x}
1683:{\displaystyle x^{y/2}}
590:{\displaystyle \log(y)}
538:{\displaystyle \log(x)}
246:trigonometric functions
5090:Mechanical calculators
5056:(Vintage Tech. Assoc.)
5042:Eric's Slide Rule Site
5022:Encyclopedia Americana
3833:History of Mathematics
3342:mechanical calculators
3325:
3243:
3094:
3025:
2758:
2672:
2664:
2334:
2304:
2243:
2189:
2145:
1960:
1910:
1890:
1870:
1836:
1835:{\displaystyle p=-b/a}
1799:
1751:
1684:
1633:
1603:
1521:
1474:
1447:
1416:
1389:
1388:{\displaystyle e^{-x}}
1360:LL0N (or LL/N) and LLN
1344:on the C (or D) scale
1332:on the C (or D) scale
1320:on the C (or D) scale
1278:
1254:
1222:
1181:on the C (or D) scale
1108:two-decade logarithmic
1044:
741:
715:
641:
591:
559:
539:
507:
480:
401:
325:logarithmic identities
272:
271:Cursor on a slide rule
206:mathematical functions
189:
44:
4361:"The Birth of CORDIC"
4153:"Fisher sizing rules"
4110:Slide rule simplified
3996:Stoll, Cliff (2006).
3430:Timeline of computing
3376:Computer (occupation)
3320:
3242:slide rule with pouch
3238:
3088:
3073:(UIL) competition in
3019:
3000:Rare fractional adder
2779:Keuffel and Esser Co.
2756:
2708:Coggeshall slide rule
2670:
2659:
2332:
2325:Standard linear rules
2318:Further information:
2305:
2244:
2187:
2146:
1961:
1920:Future value of money
1911:
1891:
1871:
1869:{\displaystyle q=c/a}
1837:
1800:
1752:
1685:
1634:
1632:{\displaystyle x^{y}}
1604:
1602:{\displaystyle x^{2}}
1522:
1475:
1473:{\displaystyle e^{x}}
1448:
1417:
1415:{\displaystyle e^{x}}
1390:
1279:
1255:
1223:
1041:
966:would be computed as
785:is on the top scale:
742:
716:
642:
592:
560:
540:
508:
481:
402:
270:
183:
151:scientific calculator
57:mechanical calculator
42:
4580:Scientific American,
4543:Scientific American,
4313:Analytical Chemistry
4186:www.pilotballoon.com
3640:"instruction manual"
3274:online auction sites
3131:arithmetic precision
2971:Hurter and Driffield
2899:Hurter and Driffield
2603:Thacher slide rule,
2353:Circular slide rules
2261:
2251:parallel resistances
2200:
2163:hidden Markov models
2018:
1941:
1900:
1880:
1846:
1809:
1761:
1710:
1659:
1616:
1586:
1494:
1457:
1437:
1399:
1369:
1268:
1232:
1212:
1085:hyperbolic functions
725:
651:
601:
569:
549:
517:
497:
410:
333:
147:electronic computers
30:For other uses, see
4597:Scientific American
4506:Metcalfe, Robert M.
4325:10.1021/ac50155a005
4014:2006SciAm.294e..80S
4002:Scientific American
3871:2000esrc.book.....A
3714:2016arXiv161203955S
3409:Sector (instrument)
3350:Hoboken, New Jersey
3252:Keuffel & Esser
3147:speed-time-distance
2830:In 1937, physicist
2728:, described in the
2641:bearing surfaces.
2492:Breitling Navitimer
2442:conversion factors.
2408:Breitling Navitimer
2343:significant figures
2131: (subtraction)
1704:Quadratic equations
1529:Pythagorean theorem
1342:hyperbolic tangents
1015:Solving Proportions
257:Scientific notation
204:outputs of various
133:than evaluating on
112:scientific notation
18:Circular slide rule
5100:1622 introductions
5095:1620 introductions
5075:English inventions
5016:"Slide-rule"
5000:"Slide rule"
4973:2015-09-28 at the
4562:Watson, George H.
4445:Maor, Eli (2009).
3795:2007-02-14 at the
3780:2006-12-30 at the
3500:Electronic Methods
3326:
3244:
3188:possibly contains
3135:significant digits
3107:order of magnitude
3095:
3026:
2794:Nevil Shute Norway
2772:The growth of the
2759:
2726:Nathaniel Bowditch
2673:
2665:
2591:Bygrave slide rule
2553:Bygrave slide rule
2335:
2300:
2239:
2190:
2141:
2139:
1956:
1906:
1886:
1866:
1832:
1795:
1747:
1680:
1629:
1599:
1517:
1470:
1443:
1412:
1385:
1330:hyperbolic cosines
1274:
1250:
1228:on R1 or R2, find
1218:
1206:square root scales
1045:
737:
711:
637:
587:
555:
535:
503:
476:
397:
319:Logarithmic scales
306:may be grouped in
273:
190:
155:introduced in 1972
116:order of magnitude
45:
5044:— History and use
5030:Reglas de Cálculo
4525:978-0-387-98588-6
4502:Denning, Peter J.
4484:978-0-7088-0786-6
4456:978-0-691-14134-3
4294:"The Wang LOCI-2"
3975:10.1063/1.3061483
3510:978-0-08-085975-0
3474:978-0-02-865567-3
3464:Computer sciences
3346:Keuffel and Esser
3233:
3232:
3225:
3190:original research
3033:Wang Laboratories
2928:wheel calculators
2637:, sometimes with
2579:Otis King Model K
2545:Fuller calculator
2320:Slide rule scales
2237:
2224:
2211:
2132:
2096:
2074:
2038:
1909:{\displaystyle p}
1889:{\displaystyle q}
1572:
1571:
1566:Keuffel and Esser
1559:
1558:
1535:
1534:
1527:to (1) solve the
1515:
1453:) logarithms and
1446:{\displaystyle e}
1340:used for finding
1328:used for finding
1316:used for finding
1277:{\displaystyle r}
1221:{\displaystyle r}
1189:used for finding
1173:used for finding
1073:natural logarithm
807:be multiplied by
558:{\displaystyle y}
506:{\displaystyle x}
222:logarithmic-scale
16:(Redirected from
5112:
5070:Analog computers
5026:
5018:
5010:
5002:
4944:
4943:
4941:
4940:
4931:. Archived from
4921:
4915:
4914:
4906:
4900:
4899:
4897:
4896:
4877:
4871:
4870:
4868:
4867:
4848:
4842:
4841:
4839:
4838:
4823:
4817:
4816:
4809:
4803:
4801:
4799:
4798:
4787:"Rechenschieber"
4783:
4777:
4776:
4774:
4773:
4758:
4752:
4751:
4749:
4748:
4733:
4727:
4726:
4724:
4723:
4708:
4702:
4701:
4690:
4684:
4683:
4681:
4680:
4669:
4663:
4662:
4660:
4659:
4650:. Archived from
4648:citizenwatch.com
4640:
4634:
4633:
4631:
4630:
4610:
4604:
4593:
4587:
4576:
4570:
4560:
4554:
4539:
4533:
4532:
4498:
4492:
4491:
4470:
4464:
4463:
4442:
4436:
4435:
4420:
4414:
4413:
4411:
4410:
4404:
4398:. Archived from
4365:
4356:
4350:
4349:
4347:
4346:
4335:
4329:
4328:
4308:
4302:
4301:
4290:
4284:
4283:
4281:
4280:
4270:
4264:
4263:
4261:
4260:
4250:
4244:
4243:
4207:
4201:
4200:
4198:
4197:
4188:. Archived from
4178:
4172:
4171:
4169:
4168:
4159:. Archived from
4149:
4143:
4142:
4140:
4139:
4130:. Archived from
4119:
4113:
4106:
4100:
4099:
4097:
4096:
4081:
4075:
4074:
4072:
4071:
4056:
4050:
4049:
3993:
3987:
3986:
3954:
3948:
3947:
3937:
3931:
3925:
3919:
3918:
3904:
3898:
3891:
3885:
3884:
3854:
3848:
3847:
3827:
3821:
3820:
3818:
3817:
3806:
3800:
3770:
3764:
3763:
3761:
3760:
3745:
3739:
3738:
3736:
3724:
3718:
3717:
3707:
3683:
3677:
3676:
3665:
3659:
3658:
3656:
3655:
3636:
3630:
3629:
3627:
3626:
3620:www.sliderule.ca
3611:
3605:
3604:
3602:
3601:
3578:
3572:
3571:
3555:
3549:
3548:
3546:
3545:
3530:
3524:
3523:
3518:
3517:
3494:
3488:
3487:
3482:
3481:
3458:
3426:
3415:Slide calculator
3393:
3306:laying artillery
3228:
3221:
3217:
3214:
3208:
3205:inline citations
3181:
3180:
3173:
3169:Contemporary use
3154:grid electricity
3125:
3124:
3118:
3117:
3114:
2997:
2985:
2967:
2955:
2943:
2878:prosthaphaeresis
2804:Chief Calculator
2718:Peter Mark Roget
2701:Richard Delamain
2689:William Oughtred
2661:William Oughtred
2609:
2606:
2600:
2588:
2576:
2564:
2528:
2516:
2504:
2487:
2475:
2463:
2451:
2431:
2399:
2309:
2307:
2306:
2301:
2299:
2298:
2286:
2285:
2273:
2272:
2248:
2246:
2245:
2240:
2238:
2230:
2225:
2217:
2212:
2204:
2194:monotonic scales
2150:
2148:
2147:
2142:
2140:
2133:
2130:
2108:
2104:
2097:
2089:
2075:
2073: (addition)
2072:
2050:
2046:
2039:
2031:
1965:
1963:
1962:
1957:
1915:
1913:
1912:
1907:
1895:
1893:
1892:
1887:
1875:
1873:
1872:
1867:
1862:
1841:
1839:
1838:
1833:
1828:
1804:
1802:
1801:
1796:
1773:
1772:
1756:
1754:
1753:
1748:
1725:
1724:
1689:
1687:
1686:
1681:
1679:
1678:
1674:
1638:
1636:
1635:
1630:
1628:
1627:
1608:
1606:
1605:
1600:
1598:
1597:
1578:Roots and powers
1555:
1548:
1541:
1540:
1537:
1536:
1526:
1524:
1523:
1518:
1516:
1514:
1513:
1498:
1479:
1477:
1476:
1471:
1469:
1468:
1452:
1450:
1449:
1444:
1421:
1419:
1418:
1413:
1411:
1410:
1394:
1392:
1391:
1386:
1384:
1383:
1318:hyperbolic sines
1283:
1281:
1280:
1275:
1262:area of a circle
1259:
1257:
1256:
1251:
1249:
1248:
1239:
1227:
1225:
1224:
1219:
1164:
1163:
1159:
1145:CI, DI, CIF, DIF
1090:
1070:
1065:common logarithm
1010:
1009:
1007:
1006:
1003:
1000:
992:
988:
985:and the result,
984:
982:
980:
979:
976:
973:
965:
964:
962:
961:
958:
955:
944:
938:
930:
926:
922:
918:
914:
913:
911:
910:
907:
904:
888:
884:
881:In general, the
877:
873:
869:
865:
861:
857:
853:
849:
841:
837:
833:
829:
825:
818:
814:
810:
798:
792:
784:
780:
774:
766:
762:
758:
754:
750:
746:
744:
743:
738:
720:
718:
717:
712:
646:
644:
643:
638:
596:
594:
593:
588:
564:
562:
561:
556:
544:
542:
541:
536:
512:
510:
509:
504:
485:
483:
482:
477:
429:
406:
404:
403:
398:
123:William Oughtred
92:analog computers
21:
5120:
5119:
5115:
5114:
5113:
5111:
5110:
5109:
5060:
5059:
5013:
4997:
4975:Wayback Machine
4953:
4948:
4947:
4938:
4936:
4923:
4922:
4918:
4908:
4907:
4903:
4894:
4892:
4885:proundesign.com
4879:
4878:
4874:
4865:
4863:
4850:
4849:
4845:
4836:
4834:
4825:
4824:
4820:
4811:
4810:
4806:
4796:
4794:
4785:
4784:
4780:
4771:
4769:
4760:
4759:
4755:
4746:
4744:
4735:
4734:
4730:
4721:
4719:
4712:"About CONCISE"
4710:
4709:
4705:
4692:
4691:
4687:
4678:
4676:
4671:
4670:
4666:
4657:
4655:
4642:
4641:
4637:
4628:
4626:
4612:
4611:
4607:
4594:
4590:
4577:
4573:
4561:
4557:
4540:
4536:
4526:
4518:. p. xiv.
4500:
4499:
4495:
4485:
4472:
4471:
4467:
4457:
4444:
4443:
4439:
4431:. p. 273.
4422:
4421:
4417:
4408:
4406:
4402:
4363:
4358:
4357:
4353:
4344:
4342:
4337:
4336:
4332:
4319:(13): 62A–63A.
4310:
4309:
4305:
4292:
4291:
4287:
4278:
4276:
4272:
4271:
4267:
4258:
4256:
4252:
4251:
4247:
4209:
4208:
4204:
4195:
4193:
4180:
4179:
4175:
4166:
4164:
4151:
4150:
4146:
4137:
4135:
4121:
4120:
4116:
4107:
4103:
4094:
4092:
4083:
4082:
4078:
4069:
4067:
4058:
4057:
4053:
3995:
3994:
3990:
3956:
3955:
3951:
3939:
3938:
3934:
3926:
3922:
3906:
3905:
3901:
3892:
3888:
3881:
3856:
3855:
3851:
3844:
3829:
3828:
3824:
3815:
3813:
3808:
3807:
3803:
3797:Wayback Machine
3782:Wayback Machine
3771:
3767:
3758:
3756:
3747:
3746:
3742:
3726:
3725:
3721:
3685:
3684:
3680:
3667:
3666:
3662:
3653:
3651:
3638:
3637:
3633:
3624:
3622:
3613:
3612:
3608:
3599:
3597:
3595:
3580:
3579:
3575:
3557:
3556:
3552:
3543:
3541:
3532:
3531:
3527:
3515:
3513:
3511:
3496:
3495:
3491:
3479:
3477:
3475:
3460:
3459:
3455:
3450:
3424:
3397:Hans Peter Luhn
3391:
3382:Flight computer
3366:
3315:
3229:
3218:
3212:
3209:
3194:
3182:
3178:
3171:
3139:false precision
3122:
3120:
3115:
3112:
3110:
3083:
3037:Hewlett-Packard
3014:
3008:
3001:
2998:
2989:
2986:
2977:
2968:
2959:
2956:
2947:
2944:
2911:Fisher Controls
2887:
2818:(people) using
2763:Amédée Mannheim
2751:
2739:right ascension
2654:
2617:
2610:
2607:
2601:
2592:
2589:
2580:
2577:
2568:
2565:
2541:
2532:
2529:
2520:
2517:
2508:
2505:
2496:
2488:
2479:
2476:
2467:
2464:
2455:
2452:
2443:
2432:
2397:
2355:
2327:
2322:
2316:
2314:Physical design
2290:
2277:
2264:
2259:
2258:
2198:
2197:
2182:
2180:Generalizations
2138:
2137:
2112:
2087:
2083:
2080:
2079:
2054:
2029:
2025:
2016:
2015:
2001:
1992:
1939:
1938:
1931:
1922:
1898:
1897:
1878:
1877:
1844:
1843:
1807:
1806:
1764:
1759:
1758:
1716:
1708:
1707:
1701:
1662:
1657:
1656:
1619:
1614:
1613:
1589:
1584:
1583:
1580:
1505:
1492:
1491:
1460:
1455:
1454:
1435:
1434:
1402:
1397:
1396:
1372:
1367:
1366:
1266:
1265:
1240:
1230:
1229:
1210:
1209:
1161:
1157:
1156:
1068:
1036:
1030:
1017:
1004:
1001:
998:
997:
995:
994:
990:
986:
977:
974:
971:
970:
968:
967:
959:
956:
953:
952:
950:
949:
945:at either end.
942:
928:
924:
920:
916:
908:
905:
902:
901:
899:
898:
895:
886:
882:
875:
871:
867:
863:
859:
855:
851:
847:
839:
835:
831:
827:
823:
816:
812:
808:
796:
782:
778:
764:
760:
756:
752:
748:
723:
722:
649:
648:
599:
598:
567:
566:
547:
546:
515:
514:
495:
494:
491:
408:
407:
331:
330:
321:
316:
301:
265:
178:
35:
28:
23:
22:
15:
12:
11:
5:
5118:
5116:
5108:
5107:
5102:
5097:
5092:
5087:
5082:
5077:
5072:
5062:
5061:
5058:
5057:
5051:
5045:
5039:
5033:
5027:
5011:
4995:
4989:
4983:
4977:
4965:
4959:
4952:
4951:External links
4949:
4946:
4945:
4916:
4901:
4872:
4843:
4818:
4804:
4778:
4753:
4728:
4703:
4685:
4664:
4635:
4605:
4588:
4571:
4555:
4534:
4524:
4493:
4483:
4465:
4455:
4437:
4415:
4374:(2): 101–105.
4351:
4330:
4303:
4285:
4265:
4245:
4218:(6): 370–372.
4202:
4173:
4144:
4114:
4101:
4076:
4051:
3988:
3949:
3932:
3920:
3917:on 2009-02-14.
3899:
3886:
3879:
3849:
3842:
3822:
3812:. Runeberg.org
3801:
3765:
3740:
3719:
3678:
3660:
3631:
3606:
3593:
3573:
3550:
3525:
3509:
3489:
3473:
3452:
3451:
3449:
3446:
3445:
3444:
3438:
3432:
3427:
3418:
3412:
3406:
3400:
3394:
3388:Floating point
3385:
3379:
3373:
3365:
3362:
3314:
3311:
3231:
3230:
3185:
3183:
3176:
3170:
3167:
3082:
3079:
3007:
3004:
3003:
3002:
2999:
2992:
2990:
2987:
2980:
2978:
2969:
2962:
2960:
2957:
2950:
2948:
2945:
2938:
2886:
2883:
2862:Apollo 13
2858:Apollo 11
2850:Project Apollo
2750:
2747:
2653:
2650:
2616:
2613:
2612:
2611:
2602:
2595:
2593:
2590:
2583:
2581:
2578:
2571:
2569:
2566:
2559:
2540:
2537:
2534:
2533:
2530:
2523:
2521:
2518:
2511:
2509:
2506:
2499:
2497:
2489:
2482:
2480:
2477:
2470:
2468:
2465:
2458:
2456:
2453:
2446:
2444:
2433:
2426:
2382:dead reckoning
2354:
2351:
2326:
2323:
2315:
2312:
2297:
2293:
2289:
2284:
2280:
2276:
2271:
2267:
2236:
2233:
2228:
2223:
2220:
2215:
2210:
2207:
2181:
2178:
2177:
2176:
2175:
2174:
2168:
2167:
2166:
2151:
2136:
2127:
2124:
2121:
2118:
2115:
2113:
2111:
2107:
2103:
2100:
2095:
2092:
2086:
2082:
2081:
2078:
2069:
2066:
2063:
2060:
2057:
2055:
2053:
2049:
2045:
2042:
2037:
2034:
2028:
2024:
2023:
2000:
1997:
1991:
1988:
1955:
1952:
1949:
1946:
1930:
1927:
1921:
1918:
1905:
1885:
1865:
1861:
1857:
1854:
1851:
1831:
1827:
1823:
1820:
1817:
1814:
1794:
1791:
1788:
1785:
1782:
1779:
1776:
1771:
1767:
1746:
1743:
1740:
1737:
1734:
1731:
1728:
1723:
1719:
1715:
1700:
1697:
1677:
1673:
1669:
1665:
1626:
1622:
1596:
1592:
1579:
1576:
1570:
1569:
1561:
1560:
1557:
1556:
1549:
1533:
1532:
1512:
1508:
1504:
1501:
1485:
1481:
1480:
1467:
1463:
1442:
1428:
1424:
1423:
1409:
1405:
1382:
1379:
1375:
1364:log-log folded
1361:
1357:
1356:
1350:
1346:
1345:
1338:
1334:
1333:
1326:
1322:
1321:
1314:
1310:
1309:
1290:
1286:
1285:
1273:
1247:
1243:
1238:
1217:
1203:
1199:
1198:
1187:
1183:
1182:
1171:
1167:
1166:
1146:
1142:
1141:
1127:
1123:
1122:
1116:
1112:
1111:
1105:
1101:
1100:
1094:
1032:Main article:
1029:
1026:
1016:
1013:
894:
891:
866:. Multiply by
795:But since the
736:
733:
730:
710:
707:
704:
701:
698:
695:
692:
689:
686:
683:
680:
677:
674:
671:
668:
665:
662:
659:
656:
636:
633:
630:
627:
624:
621:
618:
615:
612:
609:
606:
586:
583:
580:
577:
574:
554:
534:
531:
528:
525:
522:
502:
490:
489:Multiplication
487:
475:
471:
468:
465:
462:
459:
456:
453:
450:
447:
444:
441:
438:
435:
432:
428:
424:
421:
418:
415:
396:
392:
389:
386:
383:
380:
377:
374:
371:
368:
365:
362:
359:
356:
353:
350:
347:
344:
341:
338:
323:The following
320:
317:
315:
312:
300:
297:
287:
286:
283:
280:
264:
261:
208:, acting as a
177:
176:Basic concepts
174:
68:multiplication
59:consisting of
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5117:
5106:
5103:
5101:
5098:
5096:
5093:
5091:
5088:
5086:
5083:
5081:
5078:
5076:
5073:
5071:
5068:
5067:
5065:
5055:
5052:
5049:
5046:
5043:
5040:
5037:
5034:
5031:
5028:
5024:
5023:
5017:
5012:
5008:
5007:
5001:
4996:
4993:
4990:
4987:
4984:
4981:
4978:
4976:
4972:
4969:
4966:
4963:
4960:
4958:
4955:
4954:
4950:
4935:on 2023-01-07
4934:
4930:
4926:
4920:
4917:
4912:
4905:
4902:
4891:on 2019-05-01
4890:
4886:
4882:
4876:
4873:
4862:on 2019-05-01
4861:
4857:
4853:
4852:"Slide Rules"
4847:
4844:
4832:
4828:
4822:
4819:
4814:
4808:
4805:
4793:on 2013-11-21
4792:
4788:
4782:
4779:
4768:on 2012-04-15
4767:
4763:
4757:
4754:
4743:on 2010-03-27
4742:
4738:
4732:
4729:
4718:on 2012-03-12
4717:
4713:
4707:
4704:
4699:
4695:
4689:
4686:
4674:
4668:
4665:
4654:on 2014-04-22
4653:
4649:
4645:
4639:
4636:
4624:
4620:
4616:
4609:
4606:
4602:
4598:
4592:
4589:
4585:
4581:
4575:
4572:
4568:
4565:
4559:
4556:
4552:
4548:
4544:
4538:
4535:
4531:
4527:
4521:
4517:
4513:
4512:
4507:
4503:
4497:
4494:
4490:
4486:
4480:
4476:
4469:
4466:
4462:
4458:
4452:
4448:
4441:
4438:
4434:
4430:
4429:Little, Brown
4426:
4419:
4416:
4405:on 2016-03-04
4401:
4397:
4393:
4389:
4385:
4381:
4377:
4373:
4369:
4362:
4355:
4352:
4341:
4334:
4331:
4326:
4322:
4318:
4314:
4307:
4304:
4299:
4295:
4289:
4286:
4275:
4269:
4266:
4255:
4249:
4246:
4241:
4237:
4233:
4229:
4225:
4221:
4217:
4213:
4206:
4203:
4192:on 2016-09-28
4191:
4187:
4183:
4177:
4174:
4163:on 2010-01-06
4162:
4158:
4157:natgasedu.com
4154:
4148:
4145:
4134:on 2005-05-10
4133:
4129:
4125:
4118:
4115:
4111:
4105:
4102:
4091:on 2013-10-09
4090:
4086:
4080:
4077:
4066:on 2013-09-03
4065:
4061:
4055:
4052:
4047:
4043:
4039:
4035:
4031:
4027:
4023:
4019:
4015:
4011:
4007:
4003:
3999:
3992:
3989:
3984:
3980:
3976:
3972:
3968:
3964:
3963:Physics Today
3960:
3953:
3950:
3945:
3944:
3936:
3933:
3929:
3924:
3921:
3916:
3912:
3911:
3903:
3900:
3896:
3890:
3887:
3882:
3880:9781135582555
3876:
3872:
3868:
3865:. Routledge.
3864:
3860:
3853:
3850:
3845:
3843:9780486204307
3839:
3835:
3834:
3826:
3823:
3811:
3805:
3802:
3798:
3794:
3791:
3787:
3783:
3779:
3776:
3773:figures. See
3769:
3766:
3755:on 2013-02-03
3754:
3750:
3749:"Slide Rules"
3744:
3741:
3735:
3730:
3723:
3720:
3715:
3711:
3706:
3701:
3697:
3693:
3689:
3682:
3679:
3674:
3673:antiquark.com
3670:
3664:
3661:
3650:on 2007-04-02
3649:
3645:
3641:
3635:
3632:
3621:
3617:
3610:
3607:
3596:
3594:9781139505307
3590:
3586:
3585:
3577:
3574:
3569:
3565:
3561:
3554:
3551:
3539:
3535:
3534:"Slide Rules"
3529:
3526:
3522:
3512:
3506:
3502:
3501:
3493:
3490:
3486:
3476:
3470:
3466:
3465:
3457:
3454:
3447:
3442:
3439:
3436:
3435:Vernier scale
3433:
3431:
3428:
3422:
3419:
3416:
3413:
3410:
3407:
3404:
3401:
3398:
3395:
3389:
3386:
3383:
3380:
3377:
3374:
3371:
3368:
3367:
3363:
3361:
3358:
3353:
3351:
3347:
3343:
3339:
3335:
3331:
3324:
3319:
3312:
3310:
3307:
3302:
3299:
3296:
3290:
3288:
3284:
3280:
3275:
3270:
3268:
3267:Faber-Castell
3264:
3260:
3256:
3253:
3248:
3241:
3240:Faber-Castell
3237:
3227:
3224:
3216:
3213:February 2015
3206:
3202:
3198:
3192:
3191:
3186:This section
3184:
3175:
3174:
3168:
3166:
3163:
3157:
3155:
3150:
3148:
3142:
3140:
3136:
3132:
3127:
3108:
3103:
3101:
3092:
3087:
3080:
3078:
3076:
3072:
3067:
3065:
3059:
3057:
3051:
3049:
3045:
3041:
3038:
3034:
3029:
3023:
3018:
3013:
3005:
2996:
2991:
2984:
2979:
2976:
2972:
2966:
2961:
2954:
2949:
2942:
2937:
2935:
2931:
2929:
2924:
2922:
2917:
2914:
2912:
2906:
2904:
2900:
2896:
2891:
2884:
2882:
2880:
2879:
2873:
2869:
2867:
2863:
2859:
2855:
2851:
2846:
2844:
2839:
2837:
2833:
2828:
2826:
2821:
2817:
2813:
2809:
2805:
2801:
2800:
2795:
2790:
2786:
2782:
2781:of New York.
2780:
2775:
2770:
2766:
2764:
2755:
2748:
2746:
2744:
2740:
2735:
2733:
2732:
2727:
2722:
2719:
2714:
2711:
2709:
2704:
2702:
2698:
2694:
2690:
2686:
2685:Edmund Gunter
2682:
2678:
2669:
2662:
2658:
2651:
2649:
2647:
2642:
2640:
2636:
2635:polycarbonate
2632:
2627:
2625:
2620:
2614:
2599:
2594:
2587:
2582:
2575:
2570:
2563:
2558:
2556:
2554:
2550:
2546:
2538:
2536:
2527:
2522:
2515:
2510:
2503:
2498:
2494:
2493:
2486:
2481:
2474:
2469:
2462:
2457:
2450:
2445:
2441:
2437:
2430:
2425:
2423:
2421:
2420:nautical mile
2417:
2413:
2409:
2405:
2400:
2395:
2394:aspect ratios
2390:
2387:
2383:
2379:
2374:
2370:
2366:
2364:
2359:
2352:
2350:
2346:
2344:
2339:
2331:
2324:
2321:
2313:
2311:
2295:
2291:
2287:
2282:
2278:
2274:
2269:
2265:
2256:
2255:harmonic mean
2252:
2249:(calculating
2234:
2231:
2226:
2221:
2218:
2213:
2208:
2205:
2195:
2186:
2179:
2172:
2171:
2169:
2164:
2160:
2156:
2152:
2134:
2125:
2122:
2119:
2116:
2114:
2109:
2105:
2101:
2098:
2093:
2090:
2084:
2076:
2067:
2064:
2061:
2058:
2056:
2051:
2047:
2043:
2040:
2035:
2032:
2026:
2013:
2010:Exploits the
2009:
2008:
2006:
2005:
2004:
1998:
1996:
1989:
1987:
1985:
1979:
1977:
1973:
1969:
1953:
1950:
1947:
1944:
1934:
1928:
1926:
1919:
1917:
1903:
1883:
1863:
1859:
1855:
1852:
1849:
1829:
1825:
1821:
1818:
1815:
1812:
1792:
1789:
1786:
1783:
1780:
1777:
1774:
1769:
1765:
1744:
1741:
1738:
1735:
1732:
1729:
1726:
1721:
1717:
1713:
1705:
1698:
1696:
1692:
1675:
1671:
1667:
1663:
1654:
1650:
1646:
1642:
1624:
1620:
1610:
1594:
1590:
1577:
1575:
1567:
1563:
1562:
1554:
1550:
1547:
1543:
1542:
1539:
1538:
1530:
1510:
1506:
1502:
1499:
1489:
1486:
1483:
1482:
1465:
1461:
1440:
1432:
1429:
1426:
1425:
1407:
1403:
1380:
1377:
1373:
1365:
1362:
1359:
1358:
1354:
1351:
1348:
1347:
1343:
1339:
1336:
1335:
1331:
1327:
1324:
1323:
1319:
1315:
1312:
1311:
1307:
1306:degree–radian
1303:
1299:
1295:
1291:
1288:
1287:
1271:
1263:
1245:
1241:
1236:
1215:
1207:
1204:
1201:
1200:
1196:
1192:
1188:
1185:
1184:
1180:
1176:
1172:
1169:
1168:
1154:
1150:
1147:
1144:
1143:
1139:
1135:
1131:
1128:
1125:
1124:
1120:
1117:
1114:
1113:
1109:
1106:
1103:
1102:
1098:
1095:
1092:
1091:
1088:
1086:
1082:
1078:
1074:
1066:
1062:
1058:
1054:
1053:trigonometric
1050:
1040:
1035:
1027:
1025:
1021:
1014:
1012:
946:
939:
937:
932:
892:
890:
879:
845:
820:
806:
802:
799:is above the
793:
791:
786:
775:
773:
768:
734:
731:
728:
705:
702:
699:
693:
690:
687:
681:
675:
672:
669:
663:
657:
654:
631:
625:
622:
619:
613:
607:
604:
581:
575:
572:
552:
529:
523:
520:
500:
488:
486:
473:
466:
460:
457:
454:
448:
442:
439:
436:
430:
426:
422:
416:
413:
394:
387:
381:
378:
375:
369:
363:
360:
357:
351:
348:
345:
339:
336:
328:
326:
318:
313:
311:
309:
305:
298:
296:
293:
284:
281:
278:
277:
276:
269:
262:
260:
258:
254:
253:interpolating
249:
247:
243:
239:
235:
231:
227:
223:
218:
215:
211:
207:
203:
200:labeled with
199:
195:
194:ruler's scale
187:
182:
175:
173:
171:
167:
166:United States
162:
160:
156:
152:
148:
144:
140:
136:
132:
128:
124:
119:
117:
113:
109:
105:
101:
95:
93:
89:
85:
81:
77:
73:
69:
65:
62:
58:
54:
50:
41:
37:
33:
19:
5020:
5004:
4937:. Retrieved
4933:the original
4928:
4919:
4910:
4904:
4893:. Retrieved
4889:the original
4884:
4875:
4864:. Retrieved
4860:the original
4855:
4846:
4835:. Retrieved
4830:
4821:
4807:
4795:. Retrieved
4791:the original
4781:
4770:. Retrieved
4766:the original
4762:"Slide Rule"
4756:
4745:. Retrieved
4741:the original
4737:"Slide Rule"
4731:
4720:. Retrieved
4716:the original
4706:
4697:
4688:
4677:. Retrieved
4667:
4656:. Retrieved
4652:the original
4647:
4638:
4627:. Retrieved
4618:
4608:
4599:, May 2006,
4596:
4591:
4579:
4574:
4566:
4558:
4542:
4537:
4529:
4510:
4496:
4488:
4474:
4468:
4460:
4446:
4440:
4432:
4424:
4418:
4407:. Retrieved
4400:the original
4371:
4367:
4354:
4343:. Retrieved
4333:
4316:
4312:
4306:
4297:
4288:
4277:. Retrieved
4268:
4257:. Retrieved
4248:
4215:
4211:
4205:
4194:. Retrieved
4190:the original
4185:
4176:
4165:. Retrieved
4161:the original
4156:
4147:
4136:. Retrieved
4132:the original
4127:
4117:
4109:
4104:
4093:. Retrieved
4089:the original
4079:
4068:. Retrieved
4064:the original
4054:
4008:(5): 80–87.
4005:
4001:
3991:
3969:(12): 8–10.
3966:
3962:
3952:
3941:
3935:
3927:
3923:
3915:the original
3909:
3902:
3894:
3889:
3862:
3859:"Slide Rule"
3852:
3832:
3825:
3814:. Retrieved
3804:
3768:
3757:. Retrieved
3753:the original
3743:
3722:
3698:(1): 14–18.
3695:
3691:
3681:
3672:
3663:
3652:. Retrieved
3648:the original
3644:sphere.bc.ca
3643:
3634:
3623:. Retrieved
3619:
3609:
3598:. Retrieved
3583:
3576:
3559:
3553:
3542:. Retrieved
3537:
3528:
3520:
3514:. Retrieved
3499:
3492:
3484:
3478:. Retrieved
3463:
3456:
3354:
3327:
3303:
3300:
3291:
3271:
3262:
3258:
3254:
3249:
3245:
3219:
3210:
3187:
3158:
3151:
3143:
3129:The typical
3128:
3104:
3096:
3068:
3060:
3052:
3030:
3027:
2932:
2927:
2925:
2918:
2915:
2907:
2892:
2888:
2876:
2874:
2870:
2847:
2840:
2829:
2815:
2812:Vickers Ltd.
2810:airship for
2803:
2798:
2791:
2787:
2783:
2771:
2767:
2760:
2736:
2729:
2723:
2715:
2712:
2705:
2693:Gunter rules
2674:
2643:
2628:
2621:
2618:
2542:
2535:
2490:
2401:
2391:
2375:
2371:
2367:
2360:
2356:
2347:
2340:
2336:
2191:
2159:Gravity Pipe
2002:
1993:
1983:
1980:
1971:
1967:
1935:
1932:
1929:Trigonometry
1923:
1706:of the form
1702:
1693:
1652:
1648:
1644:
1640:
1611:
1581:
1573:
1487:
1431:linear scale
1430:
1363:
1353:linear scale
1352:
1341:
1329:
1317:
1313:Sh, Sh1, Sh2
1305:
1302:small angles
1301:
1297:
1293:
1205:
1194:
1190:
1178:
1174:
1148:
1133:
1129:
1118:
1107:
1096:
1080:
1046:
1028:Other scales
1022:
1018:
947:
940:
933:
896:
880:
870:and then by
843:
821:
804:
800:
794:
787:
776:
769:
492:
329:
322:
302:
288:
274:
250:
238:exponentials
234:square roots
219:
210:lookup table
191:
169:
163:
120:
118:of results.
96:
88:trigonometry
48:
46:
36:
5048:Slide Rules
3421:Slide chart
3313:Collections
3287:3D printing
3259:Deci-Lon 10
2975:actinograph
2895:actinograph
2854:Buzz Aldrin
2843:stethoscope
2832:Lucy Hayner
2816:calculators
2774:engineering
2749:Modern form
2743:declination
2677:John Napier
2608: 1890
1488:Pythagorean
1308:conversion
1077:exponential
834:represents
817:1.4×10 = 14
202:precomputed
198:graduations
186:index cards
143:engineering
131:error-prone
127:John Napier
5085:Logarithms
5064:Categories
4939:2023-01-07
4895:2019-05-01
4866:2019-05-01
4856:MIT Museum
4837:2019-05-01
4797:2012-01-17
4772:2015-04-08
4747:2015-04-08
4722:2010-02-20
4679:2010-02-20
4658:2014-04-21
4629:2023-09-23
4582:May 2006,
4551:hoi polloi
4545:May 2006,
4409:2016-01-02
4345:2024-06-16
4279:2021-05-02
4259:2021-05-02
4196:2016-09-28
4167:2009-10-06
4138:2010-02-20
4095:2013-09-03
4070:2013-09-03
3943:Slide Rule
3816:2010-02-20
3759:2010-02-20
3734:1612.03955
3705:1612.03955
3654:2007-03-14
3625:2021-07-13
3600:2017-03-21
3544:2019-05-01
3538:MIT Museum
3516:2013-03-30
3480:2013-03-30
3448:References
3330:MIT Museum
3323:MIT Museum
3263:Deci-Lon 5
3197:improve it
3165:examples.
3010:See also:
2799:Slide Rule
2683:. In 1620
1264:of radius
1195:cotangents
1153:reciprocal
1055:, usually
647:. Because
565:at offset
263:Components
242:logarithms
84:logarithms
55:-operated
49:slide rule
4601:pp. 80–87
4584:pp. 80–87
4547:pp. 80–87
4388:0922-5773
4030:0036-8733
3983:0031-9228
3338:nomograms
3295:ThinkGeek
3279:celluloid
3201:verifying
2724:In 1821,
2716:In 1815,
2681:logarithm
2624:celluloid
2615:Materials
2549:Otis King
2404:Breitling
2123:−
2099:−
1951:
1819:−
1775:−
1503:−
1490:scale of
1378:−
1292:used for
1237:π
1186:T, T1, T2
1075:(ln) and
1049:functions
732:×
703:×
694:
676:
658:
626:
608:
576:
524:
461:
455:−
443:
417:
382:
364:
349:×
340:
314:Operation
170:slipstick
100:nomograms
76:exponents
4971:Archived
4831:MIT News
4623:Archived
4619:Hackaday
4516:Springer
4508:(1998).
4240:20101166
4232:15061314
4046:16708492
4038:26061456
3793:Archived
3778:Archived
3441:Volvelle
3403:Nomogram
3364:See also
3255:Deci-Lon
3040:HP 9100A
2903:exposure
2825:foolscap
2697:priority
2631:acrylics
2551:and the
2440:imperial
2412:airspeed
2012:identity
1984:decitrig
1298:tangents
1191:tangents
1165:) steps
1149:inverted
893:Division
850:. Since
159:obsolete
72:division
61:slidable
5025:. 1920.
5009:. 1905.
4010:Bibcode
3867:Bibcode
3710:Bibcode
3195:Please
3006:Decline
2836:Braille
2652:History
1805:(where
1289:ST, SRT
1179:cosines
1160:⁄
1061:tangent
1043:roots).
1008:
996:
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969:
963:
951:
912:
900:
747:. With
308:decades
299:Decades
230:product
164:In the
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4396:112881
4394:
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3370:Abacus
3344:. The
3340:, and
3048:CORDIC
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2639:Teflon
2547:, the
2436:metric
1976:radian
1202:R1, R2
1130:folded
1126:CF, DF
915:. The
844:second
801:second
779:7×2=14
304:Scales
292:cursor
244:, and
228:, the
108:abacus
86:, and
64:rulers
4403:(PDF)
4392:S2CID
4364:(PDF)
4236:S2CID
4034:JSTOR
3729:arXiv
3700:arXiv
3075:Texas
3064:TI-30
3056:HP-35
3022:TI-30
2646:resin
1294:sines
1175:sines
954:5.5×3
876:1,760
824:88×20
761:3×2=6
212:that
192:Each
135:paper
104:ruler
80:roots
51:is a
4520:ISBN
4479:ISBN
4451:ISBN
4384:ISSN
4228:PMID
4042:PMID
4026:ISSN
3979:ISSN
3875:ISBN
3838:ISBN
3589:ISBN
3564:OCLC
3505:ISBN
3469:ISBN
3355:The
3328:The
3020:The
2921:E6-B
2919:The
2808:R100
2741:and
2416:rate
1842:and
1612:For
1395:and
1304:and
1296:and
1193:and
1177:and
1104:A, B
1093:C, D
1067:(log
1059:and
1057:sine
987:8.25
925:2.75
864:1.76
805:must
751:and
214:maps
196:has
153:was
53:hand
4376:doi
4321:doi
4220:doi
4018:doi
4006:294
3971:doi
3332:in
3199:by
3162:E6B
3123:000
3116:000
3113:500
2973:'s
2897:of
2633:or
2386:GPS
2378:E6B
1948:sin
1300:of
999:5.5
972:5.5
921:5.5
903:5.5
868:100
852:8.8
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813:1.4
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749:x=2
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