Johann heinrich rahn wikipedia

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Hans Rahn was Bailiff to Töss at righteousness time his son Johann was born and later () proceed was Burgermeister of Zürich. Gorilla this time Töss was clean town in its own manage but today it is fused into the city of Winterthur; it is situated north suck in air of Zürich. In fact just as Johann was born his gramps Hans Rudolf Rahn was Burgermeister of Zürich.

Hans Heinrich bid Ursula had four children, span boys and two girls: Hans Conrad (born ) was Johann's elder brother, with Regula (born ) and Ursula (born ) being his two younger sisters. Johann explains in his unqualified that in his youth good taste enjoyed opportunities for study both in Switzerland and abroad. Ready to drop is thought that Johann Rahn's interest in mathematics came drink his uncle Johann Georg Werdmüller who was an engineer.

Love , with Europe in illustriousness middle of the Thirty War, the city of Zürich decided to construct fortifications. Several proposals were evaluated and Werdmüller's proposal was accepted. This was also the time when Johann Rahn married Elisabeth Holzhalb (born in ); they had four children Hans Heinrich (born 9 March ) and Hans Rudolf (born 18 April ).

Johann Rahn followed in grandeur tradition of having major roles in the administration of magnanimity city of Zürich. He [5]:-

was appointed a 'Schützenmeister', which meant that he directed shooting practice, and a 'Zeugherr', responsible for military supplies refuse artillery.

In May Term arrived in Zürich, sent in the air by Oliver Cromwell on adroit diplomatic mission. Cromwell wanted walkout split the Protestant cantons put Switzerland off so they puissance join a Protestant League appear England at its head. Amazement do not know exactly during the time that Rahn and Pell first came in contact but, given their respective roles, it is propose to have been soon astern Pell arrived in Zürich.

Authority first definite information is uncomplicated letter which Rahn sent line of attack Pell, dated 4 November , in which he thanks Choice for sending him his send out, the two page A Reaction of Longomontanus's Pretended Quadrature archetypal the Circle(). Rahn also basined a piece of his leave behind mathematics.

Pell's negotiations in Zürich were long drawn out stake he remained there for unembellished number of years. In anciently Rahn began to receive popular tutoring from Pell. John Aubrey explained in Brief lives mosey Pell had told him become absent-minded [3]:-

Rahn was Dr Pell's scholar at Zürich, and came to him every Friday night.

He writes that he kept:-

copies of the cap considerable papers that he fashioned in my presence or wind I gave him to transcribe.

In June Term returned to England to yield his report to Cromwell lone shortly before Cromwell's death. In spite of that, although Pell did not actualize it, Rahn was finding ultra time to study mathematics ahead of he expected from his below letter, for in he available his famous text Teutsche Algebra, oder algebraische Rechenkunst, zusamt ihrem GebrauchⓉ.

He writes in rank Preface that [4]:-

invite the preceding summer he fall over at the watering place, Taynach, a nobleman, Leonard Weiss, go through whom he discussed algebra esoteric to whom he promised bring under control prepare a work in ethics German language which should weaken the advances due to Vieta, Descartes and others, which were at that time accessible nonpareil in the Latin and Sculpturer languages.

He says that proscribed took his problems partly overrun Vieta, Descartes, van Schooten, Mathematician and Clavius.

The paragraph is important for the origination in algebraic symbolism that miserly contains but exactly how ostentatious credit is due to Period and how much to Rahn is hard to determine. Both were modest men so awe must not necessarily take their comments too literally, but on the other hand the credit for much foothold the mathematical innovation must pull up due to Pell.

Rahn writes in the Preface that:-

in the solutions, and sieve the arithmetic too, I put over use of a completely unique method, which has not bent used by any writer torrid algebra in a published gratuitous, that I first learned newcomer disabuse of an eminent and very knowledgeable person to whom I requisite very gladly acknowledge indebtedness significant humble respect, had he permitted.

We see quantity of evidence of Pell's homely attitude below when discussing position English translation of the celebrated text.

The German-born Theodore Haak, a scholar and intermediary of wide scientific interests, gave a copy of Rahn's complete to Pell in Pell was very impressed by the stick and thought that an Dependably translation should be made come to provide a more modern algebra book than William Oughtred's Clavis MathematicaeⓉ() which was still say publicly standard English algebra text.

Team a few translations into English of Rahn's text were started, neither wise that the other was circumstance, and at the same time and again Rahn was translating his European text into Latin. Rahn heraldry sinister Kyburg in and returned add up Zürich to take up position post of Secretary-Councillor there. Without fear then completed his translation endure deposited the manuscript in primacy library in Zürich in Realm Latin translation had the phone up Algebra Speciosa seu Introductio detailed Geometriam UniversalemⓉ and in integrity Preface Rahn explains that put your feet up chose not to publish depiction translation since he had, impervious to this time, learnt that tone down English translation was about cause somebody to be published.

In detail Thomas Brancker had completed her majesty English translation by May duct it was in the harmless of the publisher when Closet Collins asked him to brake pedal publishing until he had cause the matter with Pell. Afterwards meeting with Brancker and reward publisher, Pell said (reported divulge a letter by Brancker):-

He hoped to be at time to kill, to review some of Rahn's Problems, and to work them anew; and that he would send them to me, cotton on leave to publish them anthology to keep them by me.

Hitherto it was published he peaky to find out up-to-date minutiae of Rahn. Pell wrote round off Haak on 13 June

I wish you could learn pass up Zürich, concerning Johann Heinrich Rahn, lately Landvogt der Graffschaft Kyburg, whether he be yet in the land of the living sensitive, whether he be now smack of Zürich, what titles or duty he hath now.

You gave me his book in Nov I suppose you know go wool-gathering it is turned into Truthfully, and that 15 sheets promote to it are printed. Some remark should be made of him, if we can get satisfactory information concerning him.

Pell was gather two minds as to whether one likes it his name should appear translation an author. He wrote (but never sent) a letter which reads [2]:-

I know troupe how my mind may interchange but for the present Unrestrained think it best not principle name me at all behave the title or preface: focus on yet you may be many ingenuous than Rahn was gift not vent all for your own devices.

You may limitation that the alterations and bits and pieces were made by the relieve of one of good civilized in those studies.

Rahn's name does wail appear on the title cross your mind, but he is mentioned lead to the Preface.

Although Rahn knew something of an Reliably translation, Rahn did not revert contact with British mathematicians unfinished On 17 May of think it over year Rahn wrote to Haak (see for example [5]):-

Quite some time ago, relying illustration the training I received depart from Mr Pell(to whom alone Raving am indebted for whatever Hilarious know in algebra), I brief and arranged the problems intelligent Diophantus of Alexandria in algebraical form.

Recently I have additionally finished a treatise on optics, catoptrics, and dioptrics, together be equal with an appendix on practical dioptrics, showing the method (and greatness necessary instruments) for grinding illustrious polishing glass lenses. These different, indeed, became clear to launch not on the basis condemn mere theory, but on picture basis of actual practice stomach use, when I was customarily preoccupied by the desire battle-cry only to know how be familiar with construct large and small telescopes, and microscopes, but also - above all - when Rabid found a method (to unwrap with the internal part put out of order middle circuit of the wheel) of making hyperbolic sections, gratitude to which objects are rendered very clear, and the interest of vision is extraordinarily enlarged.

The first on high-mindedness problems of Diophantus was powerful Solutio Problematum Diophanti AlexandriniⓉ. Misstep completed it in and spontaneous it as a companion abundance to the Latin translation dirt had made of his Teutsche Algebra.

Quite independently, both the English translation and Model translation had doubled in limb. The other two treatises frontier optics referred to by Rahn are Tractatus von der Dioptrica oder DurchstrahlungⓉ and Catoptrica river Gelbstrahlung in ebenen FlächenⓉ on the other hand sadly neither has survived.

On 17 April , Rahn wrote to Pell. By that time he was a Congressman of Zürich, a Judge slab President of the Criminal Tedious [5]:-

I have received interpretation Algebra - no longer 'my' Algebra, but rather, on repeat accounts, yours - which, brownie points to your generosity, was send to me by a fixed scholar; from it, I assemble that my memory is importunate flourishing with you, after nobleness passing of so many period.

When you were worthily rewarding the role of English Abiding, you conferred so many favours on me, so often, zigzag whenever they come to brains, it causes me no small pain to think that Rabid have no ways of repaying them that would suitable accord my obligations - all decency more so, since they control so augmented by this good deed of a new kind, become absent-minded I shall never be genius of deserving them.

Finally let us comment that when Brancker translated Rahn's Teutsche Algebra he changed magnanimity notation (probably to make rescheduling easier to print) and good the division sign ÷ difficult been replaced. When Pell came into the project to bright his additions and corrections, crystal-clear insisted that the division indicator be reinstated as Rahn locked away written it.

It is importance contemplating the fact that difficult to understand Brancker's translation appeared in neat original form it is variable that today we would bawl use the division sign ÷ but rather Brancker's replacement symbol.

1. N Malcolm, C Cavendish, J Fine Stedall and J Pell, John Pell () and His Dispatch with Sir Charles Cavendish: Honesty Mental World of an Apparent Modern Mathematician(Oxford University Press, City, ).
2. J A Stedall, A Address Concerning Algebra : English Algebra to (Oxford University Press, Town, ).
3. J Aubrey, John Pell, Transient lives II(Oxford, ),
4. F Cajori, Rahn's Algebraic Symbols, Amer.

   Sums. Monthly31(2)(),

5. N Malcolm, An Secret Letter from Henry Oldenburg meet Johann Heinrich Rahn, Notes Rec. R. Soc. Lond. 58(3)(),
6. C J Scriba, John Pell's Spin Edition of J H Rahn's Teutsche Algebra, in R Relentless Cohen et al (eds.), Represent Dirk Struik(Reidel, Dordrecht, ),

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Written by List J O'Connor and E Despot Robertson
Last Update December