Johann Albrecht Euler and his unpublished manuscript on the history of geometry
https://doi.org/10.22405/2226-8383-2022-23-1-236-268
Abstract
The article contains the scientific biography of J. A. Euler (1734-1800), the history and publication of the manuscript “History of Geometry” found by us with our comments. Johann Albrecht, the eldest son of Leonard Euler, was born in St. Petersburg, spent his youth with his father in Berlin, where he served as an inspector at the Berlin Observatory; at the age of 32, he with his family returned to St. Petersburg, where until the end of his life he was the conference secretary of the Imperial St. Petersburg Academy of Sciences. Huge administrative work and assistance to his blind father left him little time for independent scientific research. He retained meteorological and astronomical observations, as well as participation in his father’s home seminars on the theory of the moon and some questions of number theory. But his manuscript on the history of geometry shows the breadth of his mathematical culture, the rigor of his criteria, and the depth of knowledge of his contemporary geometry literature. Analysis of the text of the manuscript reveals the views of Euler-father and son on the history of geometry up to the 18th century, as well as the importance they attached to the applied directions of the development of geometry (astronomy, underground geometry, fortification, geodesy, cartography, auxiliary mathematical tools). The comments provide an overview of the sources used by I.A. Euler, both on the basis of direct links, and on the basis of the list of Euler’s collection and his personal contacts. For the first time, the names of many authors are introduced into the Russian historical and mathematical circulation. Despite the strong opinion that I.A. Euler, being the conference secretary of the St. Petersburg Academy of Sciences, did not have enough time for scientific work, we noted some of his important results, and also showed the range of his knowledge and
scientific criteria. For us, his work is interesting because it shows the level of development of practical geometry in the 18th century.
About the Author
Galina Ivanovna Sinkevich
Saint Petersburg State University of Architecture and Civil Engineering
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, assosiate professor
References
1. van der Waerden, B. L. 1959, Science Awakening // Moscow, GIFML.
2. Lalande J. J. 1789, Sokrashchenie astronomii ili zvezdozakoniya g. de La Landa, korolevskago chteca v mafematike, chlena akademij nauk, Korolevskoj Parizhskoj, Londonskoj, Sanktpeterburgskoj, Stokgol’mskoj, Bolognskoj i proch. i korolevskago censora. S francuzskago na rossijskoj yazyk prelozhil Mihajlo Golovin, nadvornyj sovetnik, Akademii nauk chlen i uchitel’skoj seminarii professor. – V Sanktpeterburge: pri Imperatorskoj Akademii nauk.
3. Mumenthaler, R.2009. Shvejcarskie uchyonye v Sankt-Peterburgskoj akademii nauk. XVIII vek.Sankt-Peterburg, Nestor–Istoriya.
4. Sinkevich, G. I. 2017. Rannij etap razvitiya historia matheseos. Istoriografiya istorii matematiki // Istoriya nauki i tekhniki. 1: 3–17.
5. Euler, L.1963. Pis’ma k uchyonym. Moscow–Leningrad. AN SSSR. S. 74–76.
6. Brockhaus and Efron Encyclopedic Dictionary. 1890–1907. Saint-Petersburg. Ctat’i V. V. Bobynina.
7. Iamblichus. 2002. O Pifagorovoj zhizni / per. s drevnegrecheskogo I. YU. Mel’nikovoj // Moskva, Aleteja.
8. Blancanus, J. 1615. De mathematicarum Natura dissertatio. Una cum Clarorum mathematicorum chronologia. Bologna: apud Bartholomaeum Cochium.
9. Deslandes A. F. 1737. Histoire Critique de la Philosophie. T. 2. Amsterdam: ches F. Changuion.
10. D´echalles R.P. 1778. Les El´emens d’Euclide, du R.P. D´echalles, et de M. Ozanam, De l’Acad´emie Royale des Sciences. D´emontr´es d’une maniere nouvelle & facile ; & augment´es d’un grand nombre de nouvelles Propositions & de nouveaux Usages ; & d’un Trait´e complet des Proportions arithm´etiques & des Proportions g´eom´etriques, par M. Audierne. Nouvelle Edition, revue, corrig´e & confid´erablement augment´ee par l’Auteur. A Paris, rue Dauphine,
11. Chez Cl. Ant. Jomber, fils aˆın´e ; Libraire du Roi pour le G´enie & l’Artillerie.
12. Euclidis Elementorum libri priores sex, item undecimus et duodecimus : ex versione latina Federici Commandini; sublatis iis quibus olim libri hi a Theone, aliisve, vitiati sunt, et quibusdam Euclidis demonstrationibus
13. restitutes. 1756. Pisauri: Iacobus Chriegher German: apud Camillum
14. Francischinum. Glasguae. In aedibus Academicis excudebant R. et. A. Foulis. Academiae Typographi. 1756 https://archive.org/details/euclidiselemento00eucl
15. Euclidis Megarensis Mathematici. Elementa libris XV. ad Germanam geometriae intelligentiame diversis lapsibus temporis injuria contractis restituta... Accessit decimussextus liber, de solidorum regularium sibi invicem inscriptorum collationibus. Novissime collati sunt decimusseptimus
16. et decimusoctavus, priori editione quodammodo polliciti, de componendorum, inscribendorum, et conferendorum compositorum solidorum inventis... ed. 1566, 1578. Authore Francisco Flussate Candalla. Lutetiae [Paris] : apud Iacobum Du Puys.
17. [Euclid] 1570, 1606. The elements of geometrie of the most auncient philosopher Evclide of Megara. Imprinted at London : By Iohn Daye (foreword), Billingsley, Henry, Sir, ed.
18. [Euler, L] 1976. Die Berliner und die Petersburger Akademie der Wissenschaften im Brifwechsel Leonard Eulers. Teil 3. Hrsg. u.eingel, v. A. P. Juschkewiс u. E. Winter, zum Druck vorb. v. P. Hoffmann, T. N. Klado, J. Ch. Kopeleviс. Berlin.
19. Euler, L. 1772. De solidis quorum superficiem in planum explicare licet, Novi Commentarii academiae scientiarum Petropolitanae. Volume 16. Pp. 3-34. Е419.
20. Euler, L. 1862. Leonhardi Euleri Opera postuma mathematica et physica: anno MDCCCXLIV detecta by Leonhard Euler, Academiae Scientiarum Petropolitanae. Publication date 1862. Volume 1. https://archive.org/details/leonhardieuleri00petrgoog
21. Leibniz, G. W. 1682. De vera proportione circuli ad quadratum circumscriptum in numeris rationalibus expressa. Acta Eruditorum, Februar 1682, P. 41–46.
22. Poggendorff, J. C. 1863. Biographisch-literarisches Handw¨orterbuch zur Geschichte der exacten Wissenschaften. Leipzig : J. A. Barth. Columns 704–705.
23. Reinhold, E. Manuscript 16 c. Geometria Subterranea Unter-irdische Erdm¨aßung ; oder so genannte Marck-Scheide-Kunst. Was nehmlich Selbige sey. Und Worinne die eigentlich bestehe. Nebst aufrichtigen Unterricht wie ein Geometra Subterraneus oder Markscheider bey allm f¨urkommende F¨allen richtig agieren und seinem ambte G¨ange thun soll. 3 versions: Freiberg
24. WA XVII 11, Freiberg WA XVII 677, Nachlass Scheidhauer 300m
25. Savile H. 1621. Praelectiones tresdecim in principium elementorum Euclidis. Oxford: Iohannes Lichfield & Iacobus Short.
26. Smith, D. E. 1951. History of Mathematics. Vol. 1. New York: Dover Publications Inc.
27. Souchon, C. 2003. Les cartes du Chevalier Lois-Perre Daudet aux Archives nationales un itin´eraire royal Reims-Soissons-Paris, 1722-1728 (?). CFS No 175. Mars 2003. P. 30-35.https://www.lecfc.fr/new/articles/175-article-5.pdf
28. Voigtel N. 1686 (Nachauflagen u. a. 1688, 1693). Geometria Subterranea oder Marckscheide-Kunst: darinnen gelehret wird Wie auff Bergwercken alle Kl¨uffte und G¨ange in Grundund am Tag gebracht/ auch solche voneinander unterschieden werden sollen; so wohl Was bey Durchschl¨agen in Ersparung Kosten/ Bringung Wetters und Benehmung Wassers denen Zechen oder Geb¨auden/ mit zubeoachten; Item/ Wie Streitigkeiten/ so sich unter miteinander schn¨urenden Gewercken offters zuereignen pflegen/ dem Maaße nach aus einander zusetzen; Sambt noch andern in nechstfolgendem Indice enthaltenen und zu dieser Kunst dienlichen Sachen; Allen Bergwercks-Liebenden zum Unterricht und versicherlichen Nutzen, Dietzel, Eisleben.
29. Vossius, G. J. 1650. De universae matheseos natura et constitutione liber; cui subjungitur chronologia mathematicorum. Amsterdam: ex typogr. J. Blaeu.
30. Vossius, G. J. 1660. De quatuor artibus popularibus, de philologia, et scientiis mathematicis. Cui operi subjungitur Chronologia Mathematicorum. Libri tres. Amsterdam: ex typographeio Ioannis Blaeu.
31. [Vossius] 1650. Gerardi Ioannis Vossii De quatuor artibus popularibus, de philologia, et scientiis mathematicis, cui operi subjungitur, chronologia mathematicorum, libri tres. 1650. ex typographeio Ioannis Blaeu. Caput 15. Euclidis. P. 52–53 (Separate pagination).
32. Walther H. Erasmus Reinhold. 2021 https://erasmus-reinhold-gymnasium.de/erasmus-reinhold -2/
33. Ball, W. W. R. 1889. History of the Study of Mathematics at Cambridge. Cambridge University Press, Cambridge, UK, 1889. P. 29.
Review
For citations:
Sinkevich G.I. Johann Albrecht Euler and his unpublished manuscript on the history of geometry. Chebyshevskii Sbornik. 2022;23(1):236-268. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-1-236-268
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