Background
Georg Mohr was born Jørgen Mohrendal was born on April 1, 1640, in Copenhagen, Denmark to the family of David Mohrendal, a hospital inspector and tradesman.
https://www.amazon.com/Euclides-Danicus-Amsterdam-1672-Georg/dp/B003III3IW/ref=sr_1_1?keywords=Euclides+danicus&qid=1582522801&sr=8-1
1672
https://www.amazon.com/Compendium-Euclidis-Curiosi-Meetkonstigh-passer-werck/dp/8774213377/ref=sr_1_1?keywords=Compendium+Euclidis+Curiosi&qid=1582522913&sr=8-1
1673
Georg Mohr was born Jørgen Mohrendal was born on April 1, 1640, in Copenhagen, Denmark to the family of David Mohrendal, a hospital inspector and tradesman.
Georg Mohr's parents taught him reading, writing, and basic arithmetic, but his love for mathematics could not be satisfied in Denmark, and in 1662 he went to Holland, to study mathematics with Christiaan Huygens. Where he studied, and whether he met up with Huygens is unknown. He almost certainly studied under Spinoza. He later traveled to France and England. There is no mention of any university degrees.
Georg Mohr returned to Denmark, but about 1687 he went again to Holland, this time because of a difference with King Christian V. Wishing to be scientifically independent, he remained aloof from official positions; but Tschirnhausen finally persuaded him to come to Kieslingswalde to participate in his mathematical projects. Mohr went there in 1695, accompanied by his wife, whom he had married in 1687, and by his three-year-old son. Only one of his works, the Euclides danicus (1672), a valuable short work, is known today; but his son claimed that he wrote three books on mathematics and philosophy that were well received by scholars.
What Georg Mohr did to support himself is unknown for most of his life. He enjoyed being a free, learned man, and did not want to be tied down to a government job that would interfere with his scientific work. A reasonable guess is that he taught to support himself. It is clear that he settled in Holland after studying (presumably) there. He fought in the Dutch-French conflict of 1672-1673 and was taken prisoner. Sometimes, perhaps directly after the war or around 1681, he returned to Denmark where the King offered to make him supervisor of royal shipbuilding. He refused and returned to Holland around 1687.
In 1695-1697, finally, after resisting for several years, he accepted a job at Tschirnhaus's little museion in Kieslingswalde. This appears clearly to have been an arrangement of patronage.
Mohr is often mentioned in the intellectual correspondence of the day. He corresponded with Leibniz, with Pieter van Gent, and with Ameldonck Bloeck, a member of Spinoza’s circle. In 1675 Oldenburg sent Leibniz a work of Mohr’s on the root extraction of Leibniz, in a letter of 1676 to Oldenburg in which he refers to “Georgius Mohr Danus, in geometria et analysi versatissimus,” mentions that he learned from Mohr that Collins had the expansions for sin x and arcsin x. Unfortunately, little else of Mohr’s scientific activity is known.
In 1928 Mohr’s Euclides danicus, which had fallen into obscurity, was republished with a preface by J. Hjelmslev. Hjelmslev recognized that in 1672 Mohr had been dealing with a problem made famous 125 years later by Mascheroni, namely, that of making constructions with compass alone.
The book has two parts: the first consists of the constructions of the first six books of Euclid; the second, of various constructions. The problem of finding the intersection of two lines, which is of some theoretical importance, is solved incidentally in the second part in connection with the construction of a circle through two given points and tangent to a given line.
Hjelmslev made the acute observation that a minor variant of Mohr’s constructions enables one to add and subtract segments on the sphere and in the hyperbolic plane.
The obscurity that befell Mohr and his Euclides Danicus can be attributed, in some degree, to the presentation of the material. In the body of the book, Mohr does not state the issue until the very last paragraph, although the lines are referred to as “imagined” (gedachte). In the dedication to Christian V, he does say that he believes he has done something new, and on the title page, the issue is explicitly stated. Still, it would be easy for an inattentive reader to misjudge the value of the book.
According to Hjelmslev, Mascheroni’s result - that all ruler and compass constructions can be done by compass alone - was already known and systematically expounded by Mohr. (The justice of this judgment and the question of the independence of Mascheroni’s work are examined in the article on Mascheroni.)
The laconic Mohr tells us nothing about the genesis of his ideas. A guess is that the fundamental problem stems from a similar problem, that of the compass of a single opening, which was posed in the contests of the great Renaissance mathematicians.
Georg Mohr was married and had a son.
