[←18]
Friedrich Wilhelm August Murhard (1799–1853) received his Ph.D. at Göttingen in 1796 and had been Privatdozent in mathematics there. His Bibliotheca mathematica (5 vols.; Leipzig, 1797–1805), valuable even today, is a famous proof of his far-reaching knowledge of literature. In 1798 he left Göttingen on a long journey which led him to Asia Minor. He plagiarized and dedicated the book to the emperor, was arrested in Hungary for idle babblings about government and religion, and made a translation of Lagrange’s Mécanique analytique. Later Murhard led a varied and adventurous life as a political and journalistic writer.
[←19]
Urban Friedrich Benedict Brückmann (1728–1812), professor of anatomy and ducal physician in Brunswick, had a special collection of precious stones.
[←20]
Georg Friedrich von Tempelhoff (1737–1807), who is mentioned in the letter, was a Prussian artillery officer, member of the Berlin Academy of Sciences, and published a textbook on algebra in 1773,
[←21]
Johann Heinrich Jakob Meyerhoff (1770–1812) became in 1794 collaborator, and in 1802 director, of the gymnasium in Holzminden. He was thoroughly grounded and trained in the ancient and modern languages. As a Göttingen student he had won a golden prize medal for a Latin dissertation on the Phoenicians. Yet mathematics was rather foreign to him.
[←22]
The chronology of the eight Gaussian proofs of the fundamental theorem, dating them according to the time of their publication and counting them as Gauss does, is—
Proof I (Disquisitiones, Article 135 et seq,; Works, Vol. I, p. 104):
1801
Proof II (Disquisitiones, Art. 262, Works, Vol. I, p. 292):
1801
Proof III (Royal Soc. of Göttingen, Works, Vol. II, p. 1):
1808
Proof IV (Royal Soc. of Göttingen, Works, Vol. II, p. 9):
1811
Proofs V & VI (Royal Soc. of Göttingen, Works, Vol. II, p. 47):
1818
Proofs VII & VIII (posthumous, Works, Vol. II, p. 234):
1863
Proof I dates from April 8, 1796, and Proof II from June 7, 1796, Proofs VII and VIII (really one full proof) are at the latest September 2, 1796, Proof IV dates from May 15, 1801; the remainder of the proofs originated after 1805, but the exact date of the discovery of each is uncertain.
[←23]
Gauss, Collected Works, II, 188,
[←24]
Heinrich Wilhelm Matthias Olbers was born October 11, 1758, at Arbergen on the Weser, a village near Bremen, where his father was a pastor. He studied medicine at the University of Göttingen during the years 1777–1780, at the same time attending Kästner’s lectures on mathematics. In 1770, while watching by the sickbed of a fellow student, he devised a method of calculat ing cometary orbits which made an epoch in the treatment of the subject, and is still extensively used. This important discovery was published by Baron von Zach with the title Ueber die leichteste und bequemste Methode die Bahn eines Cometen zu berechnen (Weimar, 1797). A table of 87 orbits was attached, increased to 178 by Encke in the second edition (1847), and to 242 by Galle in the third (1864 and 1894).
About the end of 1781 Olbers settled as a physician in Bremen; in June, 1785, he married Dorothee Elisabeth Köhne, who died in less than one year, having fourteen days previously given birth to a daughter, Doris, who married the lawyer Dr. Christian Focke, and died in 1818, She had six children, and through her Olbers had seven great-grandchildren during his lifetime. In 1789 Olbers married Anna Adelheid Lürssen (born in 1765); one son, Senator Georg Heinrich Olbers, was born on August 11, 1790, and survived his father, who died March 2, 1840, Anna Lürssen Olbers died on January 23, 1820,
Olbers practiced medicine actively for forty years in Bremen and retired on January 1, 1823, He is said never to have slept more than four hours, the major portion of each night being given over to astronomy. The upper part of his house was fitted up as an observatory. He gave special attention to comets, and that of March 6, 1815, (period, seventy-four years) was named for him, in memory of its discovery by him.
His bold hypothesis of the origin of the minor planets by the disruption of a primitive large planet (Monatl. Corr. VI, 88), although later discarded, was strengthened by the finding of Juno by Harding and of Vesta by himself, in the precise regions of Cetus and Virgo where the nodes of such supposed planetary fragments should be situated. Olbers was deputed by his fellow citizens to assist at the baptism of the King of Rome on June 9, 1811, and was a member of the corps législatif in Paris 1812–1813, besides being a member of many learned societies. He received decorations from the governments of various countries, and a monument was erected in Bremen to his memory. In 1828, the largest ship which had ever left Bremen (up to that time) was named Olbers, for him, and carried a thousand German emigrants to Brazil. It was wrecked in 1837,
He was the eighth of sixteen children. His father became preacher of the Domkirche in Bremen in 1760 and died in 1772, Olbers attended the Gymnasium in Bremen; his preference for astronomy showed itself when he was fourteen years of age. At the age of nineteen he observed the solar eclipse of 1777, At Göttingen he computed the orbit of the comet of 1779, His doctor’s thesis of 1780 was entitled De oculi mutationibus internis. In 1781 he made a trip to Vienna, where he gained admission to the observatory under Maximilian Hell, and for the first time, on August 17, 1781, saw the planet Uranus, discovered that year by Herschel, even before the Vienna astronomers saw it.
His home in Bremen was at Sandstrasse 16, He had a large medical practice and at ten o’clock in the evening would withdraw to his private observatory. A monument was erected to his memory on the wall-promenade in 1850,
[←25]
Sophie Germain was born on April 1, 1776, the daughter of a well-to-do Parisian family. She was just thirteen years old when the Revolution broke out and would frequently take refuge in her father’s library during those days. One day Montucla’s History of Mathematics fell into her hands. Here she read of Archimedes’ death. The story made a deep impression on her. In order to study Newton and Euler, she learned Latin without a teacher’s instruction. When the Ecole Polytechnique was opened, she smuggled her own mathematical papers in among those of the male students under the pseudonym of Le Blanc, and the professor, no less a person than Lagrange, found the work of this Le Blanc so praiseworthy that he became her adviser in studies, when he found out who the author was. Thus she became a city celebrity; great scholars visited her at her father’s home. In 1799 appeared Legendre’s Theory of Numbers, and when Gauss’ work appeared nearly three years later she was prepared to present to him the results of her own research in the subject, as a result of study of the two volumes. She again used the pseudonym, because at that time a learned woman was hardly taken seriously. But when Brunswick was taken by the French and she became worried about the safety of the young mathematician there, “Le Blanc” was laid aside, and she appealed to General Pernety, who was a friend of her family.
Sophie Germain’s most important accomplishments are in the field of the theory of numbers. To be sure, she reaped the greatest honors with a problem in the theory of surfaces and mathematical physics, for which the Paris Academy of Sciences had set up a prize by order of Napoleon. A mathematical theory of elastic surfaces was sought, a result of Chladni’s physical experiments. Sophie Germain received the prize. Her paper has today only historical value. She died of cancer, on June 27, 1831, aged fifty-five. When the matter of honorary degrees came up in 1837 at the centenary celebration of the University of Göttingen, Gauss regretted exceedingly that Sophie Germain was no longer alive. “She proved to the world that even a woman can accomplish something worth while in the most rigorous and abstract of the sciences and for that reason would have well deserved an honorary degree,” he said.
[←26]
Ch. Z. Slonimsky so expanded the latter formula that it gives any requir
ed information about the Jewish calendar of any year, in Crelle’s Journal, Vol. 28 (1844), p. 179, M. Hamburger gave the first thorough proof in Crelle’s Journal, Vol. 116 (1896), p. 90.
[←27]
Bessel was the son of Karl Friedrich Bessel, who studied law in Göttingen and held various governmental positions, dying in 1829 or 1830, The mother was Charlotte Schrader, daughter of a pastor in Hausberge, near Minden. She died in 1814, Franz (usually written Friedrich) Wilhelm Bessel was the second of nine children, born on July 21, 1784, at Minden. He attended the gymnasium in Minden and left it when fourteen years of age “because he could not enter into friendship with Latin.” After some private instruction, he was in the employ of A. G. Kuhlenkamp and Sons in Bremen as a clerk, from January 1, 1799, to March 19, 1806, As he intended to go to isea on a merchant vessel, he studied navigation and thus was led to astronomy. His first work was published in von Zach’s Monatl. Corr. in 1804, “Computation of Harriot’s and Torporley’s Observations of the Comet of 1607,” In 1806 he went to take Harding’s place as inspector of the Lilienthal observatory on the Worpe, near Bremen. While there he wrote some valuable memoirs, especially the “Investigation of the True Elliptic Motion of the Comet of 1769,” He remained there until March 27, 1810, At Easter, 1810, he moved to Königsberg to become full professor of astronomy and take charge of the erection of a new observatory. His sister, Augusta Dorothea Amalie, accompanied him. In 1812 Bessel married Johanna Hagen, daughter of a well-known Königsberg professor of chemistry. She was born March 20, 1794 and died about 1885, He had one son, Karl Wilhelm (June 16, 1814–October 26, 1840), and three daughters.
[←28]
Sent through the Bethmann Bank.
[←29]
Heinrich Christian Schumacher, son of Andreas Anthon Friedrich Schumacher, was born at Bramstedt in Holstein on September 3, 1780, In 1813 he married Christine Magdalene von Schoon. From 1817 on he directed the triangulation of Holstein, and later a complete geodetic survey of Denmark (completed after his death). For the survey an observatory was established at Altona, and Schumacher resided there permanently, chiefly occupied with the publication of ephemerides (eleven parts, 1822–1832) and of the Journal Astronomische Nachrichten, of which he edited thirty-one volumes. He died at Altona on December 28, 1850,
His nephew, Christian Andreas Schumacher (1810–1854), was associated with the geodetic survey of Denmark from 1833 to 1838 and afterward 1844–1845) improved the observatory at Pulkowa.
H. C. Schumacher’s son Richard 1827–1902) was his assistant from 1844 to 1850 at the Altona observatory. Having become assistant to Carlos Guillelmo Moesta (1825–1884), director of the observatory at Santiago, in 1859, he was associated with the Chilean geodetic survey in 1864, Returning in 1869, he was appointed assistant astronomer at Altona in 1873, and afterward at Kiel.
[←30]
Carl Haase (December, 1817-March 23, 1877) translated the Latin original into German in 1864 with the title Theorie der Bewegung der Himmelskorper, welche in Kegelschnitten die Sonne umlaufen, and published it at Hanover in 1865, The English translation was published in 1857 at Boston by Rear Admiral Charles Henry Davis, assistant in the U.S. Coast Survey in 1842 and later superintendent of the Naval Observatory.
[←31]
There has been some confusion as to the discoverer of these formulas. It seems that Delambre discovered them in 1807, but did not publish them until 1809 in the Connaissance des temps, p. 443, They were discovered independently by Gauss, and are often called “Gauss’ equations.” Both systems may be proved geometrically. The geometric proof is the one originally given by Delambre. It was rediscovered by Professor Crofton in 1869, and published in the Proceedings of the London Math. Soc, Vol. II. (See Casey’s Trigonometry, p. 41,) Carl Brandon Mollweide (1774–1825) of Leipzig had also published them before 1809,
[←32]
See Appendix B.
[←33]
Olaus Romer of Copenhagen had in the seventeenth century constructed a meridian circle of wood, but it was lost in a fire.
[←34]
Removed in 1945,
[←35]
Börsch and Simon edited a German text of Gauss’ memoirs on the method of least squares (Berlin, 1887); J. Bertrand published a French text of these memoirs (Paris, 1855).
[←36]
1 Georg Ernst Friedrich Hoppenstedt (1779–1858).
[←37]
He lived at Prinzenstrasse 3 in the years 1831–1837, and at Jüdenstrasse 40 in the years 1848–1891,
[←38]
The Gauss Archive in Göttingen possesses five letters from Sir David to Gauss, dated 1816–1854,
[←39]
Quetelet was on journey making measurements of terrestrial magnetism in Holland, Germany, Italy, and Switzerland.
[←40]
It covered forty-seven pages.
[←41]
Gauss’ entry states: “7 a.m. before getting up.”
[←42]
It was not chosen as the prize question.
[←43]
J. F. C. Hessel (1796–1872), professor of geology and mineralogy in Marburg. In his next letter Gerling explained to Gauss that Hessel’s manuscript had been brought into disorder at the printer’s but the proofreader had not noticed it.
[←44]
Both Gauss and his son Joseph were nearsighted.
[←45]
Other than the editors of his Collected Works.
[←46]
He was declared legally dead in 1827,
[←47]
XVII, 295,
[←48]
Vol. 25, part 3 (1840), pp. 147 et seq.
[←49]
He had ordered one copy after reading the review in Gersdorf’s Repertorium; Otto Struve, son of Wilhelm, had later given him the other one.
[←50]
Gauss wrote just before the jubilee that a deluge of poems had “broken out.
[←51]
Johann Friedrich Ludwig Göschen (1778–1837), professor of law.
[←52]
Ludolf Dissen (1784–1837), professor of classical philology.
[←53]
November 1, 1837,
[←54]
In a letter to Olbers he wrote that Paris was the last place to which he would go.
[←55]
At a banquet the King told Humboldt: “For my money I can have as many ballet dancers, whores, and professors as I want.”
[←56]
After his death it was given to Joseph.
[←57]
Act I, Scene II. The word “law” was altered to “laws.”
[←58]
Göttingische gelehrte Anzeigen.
[←59]
He stated his full views on the imaginary in a letter to Bessel dated December 18, 1811,
[←60]
Refers to Gauss’ general theory of terrestrial magnetism.
[←61]
P. H. L. Boguslawski (1789–1851), professor of astronomy and director of the observatory at Breslau.
[←62]
L. Kronecker, Vorlesungen, II, ed. Hensel (1901), p. 42,
[←63]
Low German for “pipe.”
[←64]
German: ins Wasser fallen.
[←65]
Euler and Vandermonde.
[←66]
Students referred to him as a Zeitungstiger.
[←67]
For years he used a special brand of French wine.
[←68]
He also used Schmidt’s Russian-German Dictionary (Leipzig, 1842).
[←69]
Gauss made a thorough study of Goethe’s Farbenlehre.
[←70]
It was Spinoza. See Tractatus politicus, Chapter I, paragraph 4,
[←71]
The National Assembly, 1848–1849, met in this church at Frankfurt.
[←72]
The King of Prussia.
[←73]
He studied Böhmer’s
Kaiser Friedrichs III Entwurf einer Magna Charta für Deutschland.
[←74]
This statement is inaccurate. His investments in Austrian bonds amounted to 26,604 thalers, out of an estate of 152,892 thalers.
[←75]
It was a circular table of 47 inches diameter; the feet formed an equilateral triangle, each side of which was 23 inches.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 57