17th century in the history of informatics

Scottish mathematician JOHN NEPER (John Naiper, 1550 - 04.04.1617) invented tables of logarithms . Their principle is that each number corresponds to a special number - the logarithm is the exponent to which the number must be erected (the base of the logarithm) in order to obtain a given number. In this way, you can express any number. Logarithms greatly simplify division and multiplication. To multiply two numbers, it suffices to add their logarithms. Due to this property, a complex multiplication operation is reduced to a simple addition operation. For simplification, tables of logarithms were compiled, which later were built into a device that allows to significantly speed up the calculation process, a slide rule.

Napier proposed in 1617 another (non-logarithmic) method of multiplying numbers. The tool, called Napier's wand (or knuckles), consisted of thin plates or blocks. Each side of the block carries numbers that form a mathematical progression. Manipulations with blocks allow you to extract square and cubic roots, as well as multiply and divide large numbers.

Magazine "Submarine" №8-1998 NEPER - NA PEER!

Newspaper "INFORMATIKA"

JUST A LINE (John Napier, Edmund Gunther, Edmund Wingate, William W. Otred, Richard Delamein, William Forster, Richard Delameyn, Robert Bissacker, Seth Patridge, John Robertson, Amedey Mannheim - all of these names are associated with a logarithmic string

In 1620, the Swiss mathematician JostBurgi, who worked in Prague, independently of Napier, published his table of logarithms.

Naper's sticks

Fragment of Edmund Gunter line

In 1618, the English mathematician and astronomer Edmund Gunter (Edmund Gunter, 10.12.1581–1626) proposed a mechanical device using a logarithmic scale to facilitate calculations. Two scale-gauges were attached to several scales graduated exponentially, which had to be operated simultaneously, determining the sum or difference of segments of the scale, which made it possible to find a work or a quotient. These manipulations required increased attention.

General view of the Edmund Gunter line

In 1957, the German scientist Franz Gammer discovered a photo of a sketch of the invention of Professor Wilhelm Schickard, which was dated 1623. It automatically performed addition, subtraction, multiplication, and division. Using the materials found, in the early 60s, scientists recreated a working model of the Schickard machine.

Wilhelm Schickard (Wilhelm Schickard, 04.22.1592 - 10.24.1636) - an orientalist and mathematician, professor at Tyube University - in letters to his friend Johann Kepler described a “counting clock” device - a counting machine with a number setting device and rollers with a slider and a window for reading the result.
It was a very “advanced” 6-bit machine, which consisted of three nodes: an addition-subtraction device, a multiplying device, and a block for recording intermediate results. If the adder was made on traditional gears that had cams for transferring the transfer unit to the next digit, then the multiplier was built very sophisticatedly. In it, the German professor applied the “lattice” method, when with the help of a gear “multiplication table” mounted on shafts, each digit of the first factor multiplied by each second is multiplied, after which all these private works are shifted.

However, it is not known whether Shiccard himself was able to build his adding machine. There is evidence in his correspondence with astronomer Johannes Kepler (Johannes Kepler, 1571–1630) that an unfinished model died in a fire during a workshop fire. In addition, the author, who soon died of cholera, did not manage to introduce information about his invention into scientific use, and it became known only in the mid-twentieth century.

Magazine "Submarine" №3-1998 ABOUT THE ART OF READING FOREIGNS BY LETTERS

Newspaper "INFORMATIKA"

WILHELM SHIKKARD

MECHANICAL CALCULATORS (The creation of the first mechanical counting devices associated with the names of V. Shikkarda, B. Pascal and G. Leibniz)

Hives out

The inventors of the first logarithmic lines are the British - mathematician and teacher William Othred (William Oughtred, 03/05/1574 - 06/30/1660) and the mathematics teacher Richard Delameyn (Richard Delamain, 1600–1644). Apparently, William Outred and Richard Delameyn invented the slide rule independently of each other. In the slide rule, the scales shifted relative to each other, and therefore, in the calculation, there was no need to use such a burden as compasses. Moreover, the British proposed two designs: rectangular and round, in which the logarithmic scales were applied on two concentric rings rotating relative to each other. In 1632 in London, the book of Otred and Forster “Circles of Proportions” was published with a description of the circular slide rule, and the description of the rectangular slide rule of Regen was given in the book of Forster “Addition to the use of the tool called Circles of Proportions”, published next year. The rights to manufacture their own lines were presented by Otred to the famous London mechanic Elias Allen.

The newspaper "INFORMATIKA" INVENTORS LINEEK

The ruler of Ulyam Otred

The French mathematician BLEZ PASCAL (Blaise Pascal, June 19, 1962–19.08.1662) designed a counting device to facilitate the work of his father, a tax inspector. This device allowed to add decimal numbers. Externally, it was a box with numerous gears.

The basis of the summing machine was the counter-recorder, or counting gear. She had ten protrusions, each with figures. For the transfer of tens, there was one elongated tooth on the gear, which hooked and turned the intermediate gear, which transmitted the rotation of the gear of tens. Additional gear was necessary for the two counting gears - units and tens - to rotate in the same direction.

Counting device Pascaline

The counting gear with a ratchet mechanism (transmitting direct movement and not transmitting the reverse) connected to the lever. The deviation of the lever at one angle or another allowed entering single digits into the counter and summing them up. In Pascal's car, a ratchet drive was attached to all of the counting gears, which made it possible to sum up multi-digit numbers.

Magazine "Submarine" №4-1998 TWO EVENINGS AT HERZOGHINI D'EGIYON

Newspaper "INFORMATICS" MECHANICAL CALCULATORS (The creation of the first mechanical counting devices associated with the names of V. Shikkard, B. Pascal and G. Leibniz)

The British Robert Bissakar (Robert Bissaker), and in 1657 - regardless of him - Seth Patridzh developed a rectangular slide rule, the design of which has largely been preserved to this day.

Ruler Robert Bissakar, 1654

The device line consisted of three strips. Each strip had a length of about 60 cm; two outer straps were held together by a metal frame, and the third (slider) slid between them. Each scale on the fixed slats corresponded the same on the engine. Scales were on both sides of the ruler. Here are just a slider that recorded the result of the operation, this design does not provide. The great sir Isaac Newton (Isaac Newton, 1643–1727) spoke of the need for this, of course, a useful element in 1675. However, his absolutely fair wish was realized only a century later.

Newspaper "INFORMATIKA"
JUST A LINE (John Napier, Edmund Gunther, Edmund Wingate, William W. Otred, Richard Delamein, William Forster, Richard Delameyn, Robert Bissacker, Seth Patridge, John Robertson, Amedey Mannheim - all of these names are associated with a logarithmic string

Gottfried Wilheim Leibniz

German philosopher, mathematician, physicist GOTFRID WILGEIM LEIBNITZ (Gottfried Wilhelm Leibniz, 07/01/1646 - 11/14/1716) created a "step calculator" - a counting machine that allows you to add, subtract, multiply, divide, extract square roots, using a binary system, which uses a dual system .

The first arithmometer Leibniz made in 1673. After that, more than 20 years engaged in the improvement of his counting machine. The result of the intense search 8-bit model could add, subtract, multiply, divide, raise to a power. The result of multiplication and division was 16 characters. Leibniz used in his arithmometer such constructive elements that were used in the design of new models until the twentieth century. First of all, it is necessary to attribute the movable carriage to them, which made it possible to significantly increase the speed of multiplication. The management of this machine was extremely simplified due to the use of the handle, with the help of which the shafts rotated, and the automatic control of the number of additions of private works during multiplication.

In the 17th century, of course, there could be no question of the serial production of Leibniz calculators. However, they were released not so little. For example, one of the models went to Peter I. The Russian Tsar ordered the mathematical machine in a very peculiar way: he presented it to the Chinese emperor for diplomatic purposes.

The car was the prototype of the adding machine, used from 1820 until the 60s of the twentieth century.

Magazine "Submarine"
№10-1998 SEARCHING FOR LINGUA GENERALS
№7-1999 HISTORY OF THE ORIGIN AND CREATION OF DIFFERENT COMPUTING MACHINES

Journal "Home Computer"
№08-2002 MECHANIZATION
№10-2002 PRASHUR

Computerworld Magazine
№17-2001 CHARLES BEBBIDGE - INVENTOR AND ... POLITECONOM
№42-2002 TERRACE MACHINE IN THE XIX CENTURY (Against the backdrop of such a bright star, Babbage often forget about smaller stars. In parallel with him, developing this trend, several more inventors worked at the end of the 18th century and the first half of the 19th century).

Newspaper "INFORMATIKA"
ARISTOTLE, LEIBNITZ, BUL
MECHANICAL CALCULATORS (The creation of the first mechanical counting devices associated with the names of V. Shikkarda, B. Pascal and G. Leibniz)
FAMOUS ANGLISHANIN (One of the most prominent figures in science and technology of the XIX century was the Englishman Charles Babbage)

Moreland Machines

Jonas Moore, the London cartographer, mechanic and teacher, so recommended in the “Mathematical Compendium” of Morland’s machine he wrote : “If gentlemen or other persons, especially ladies, who have not had time to practice numbers, will want to figure out their payments or expenses, they can to obtain from Mr. Humphrey Adamson, who lives near Turnstile in Hoelbourn, incomparable instruments that will show them how to add and subtract pounds, shillings, pence and whole numbers without pen, ink and memory costs; these tools are the invention of the most worthy man, the decoration of his country, Sir Samuel Moreland, the baronet. ” This meant that Sir Samuel Morland (Samuel Morland, 1st Baronet, 1625 - 12/30/1695) offered the Briton the world's first non-decimal computing machine that knew how to work with English currency. It was suggested to enter data not from the keyboard, but from a certain similarity of typesetting disks.

Magazine "Submarine" № 2-1998 WHO INVENTED THE WHEEL?

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Sir Samuel Morland

Thomas Everard proposed a ruler for measuring volumes with two engines and a newly introduced inverse scale.