''Euclides Danicus'' (the Danish Euclid) is one of three books of mathematics written by

Georg Mohr Jørgen Mohr (Latinised ''Georg(ius) Mohr''; 1 April 1640 – 26 January 1697) was a Danish mathematician, known for being the first to prove the Mohr–Mascheroni theorem, which states that any geometric construction which can be done with co ...

. It was published in 1672 simultaneously in

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

and

Amsterdam Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population ...

, in Danish and Dutch respectively. It contains the first proof of the Mohr–Mascheroni theorem, which states that every geometric construction that can be performed using a

compass and straightedge In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an ideali ...

can also be done with compass alone.. The book is divided into two parts. In the first part, Mohr shows how to perform all of the constructions of

Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Elements'' treatise, which established the foundations of ...

's ''Elements'' using a compass alone. In the second part, he includes some other specific constructions, including some related to the mathematics of the

sundial A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a fl ...

. ''Euclides Danicus'' languished in obscurity, possibly caused by its choice of language, until its rediscovery in 1928 in a bookshop in Copenhagen. Until then, the Mohr–Mascheroni theorem had been credited to Lorenzo Mascheroni, who published a proof in 1797, independently of Mohr's work. Soon after the rediscovery of Mohr's book, publications about it by Florian Cajori and

Nathan Altshiller Court Nathan Altshiller Court (1881-1968) was a Polish-American mathematician, a geometer in particular and author of the famous book ''College Geometry - An Introduction to the Modern Geometry of the Triangle and the Circle''. Biography Nathan Court w ...

made its existence much more widely known.. The Danish version was republished in facsimile in 1928 by the

Royal Danish Academy of Sciences and Letters {{Infobox organization , name = The Royal Danish Academy of Sciences and Letters , full_name = , native_name = Det Kongelige Danske Videnskabernes Selskab , native_name_lang = , logo = Royal ...

, with a foreword by Johannes Hjelmslev,. and a

German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...

translation was published in 1929. Only eight copies of the original publication of the book are known to survive. In 2005, one of these original copies was sold at auction, to

Fry's Electronics Fry's Electronics was an American big-box store chain. While operating, it was headquartered in San Jose, California in Silicon Valley. Fry's retailed software, consumer electronics, household appliances, cosmetics, tools, toys, accessories, ma ...

, for what Gerald L. Alexanderson calls a "ridiculously low price": US$13,000.

References

Wikicommons has a copy of the original: https://commons.wikimedia.org/wiki/File:Georg_Mohr%27s_Euclides_Danicus.pdf

References

Further reading