REGIOMONTANUS. 



REONARD, JEAN-FRANCOIS. 



composed his work entitled ' De Triangulis Planis et Sphscricis,' first 

 published at Niirnbcrg in 1533, folio, fifty-seven years after the author's 

 death, which is now the most interesting of his works. It contained 

 two tables of natural sines, one to a radius 6,000,000, the other to a 

 radius 10,000,000, and by their means all the cases of plane and 

 spherical triangles were solved, without the aid of a similar table of 

 tangents, the utility of wliich he did not perceive, and the consequence 

 of which oversight was that the solutions, though occasionally very 

 ingenious, are in most cases excessively prolix. The solution of that 

 case of spherical triangles in which, the angles being known, it is thenco 

 required to determine the sides, was first given in this work. The 

 trigonometry and the tables of sines appear to have been published 

 separately. The title of the latter, according to Nieeron, was ' Com- 

 positio Tabularum Sinuurn, cum Tabulis Duplicibus Sinuum ejusdem,' 

 fol., Niirnb., 1541. A detailed analysis of the trigonometry is given 

 in the ' Astronomie du Moyen Age,' pp. 292-323 and 347. It affords, 

 says Delambre, a very complete view of what was then known of plane 

 and spherical trigonometry, though the discoveries in this branch of 

 science, which belonged exclusively to Miiller, were not of great 

 importance. While in Italy he likewise detected many errors in 

 Trebizond's version of the ' Almagest,' which he severely criticised. 

 This excited so much animosity, that some have attributed Muller's 

 early death to poison administered to him by one of the sons of 

 Trebizond. (Vossius, 'De Scientiis Mathematicis,' p. 184.) 



The earliest edition of Purbach and Muller's translation of the 

 'Almagest ' appears to be that of Venice, fol., 1496. It was reprinted 

 at Basel in 1543, and there are several subsequent editions. The title 

 of the two editions mentioned is ' Joaunis de Monte Regio et Georgii 

 Purbachii Epitome in Cl. Ptolemcei Magnam Compositionem, continens 

 Propositiones et Aunotatioues quibus totum Almagestum declarator.' 

 The first six books were the work of Purbach, who makes the length 

 of the sidereal year 365 days, 6 hours, 9 miuutes, 12 seconds, which 

 is much nearer the truth than that given by his predecessors. He 

 also states that the obliquity of the ecliptic given by Ptolemseus is 

 23 51' 20", but that in his own time he is unable to make it more than 

 23 28', though he does not say whether he considers the obliquity to 

 be decreasing or Ptolemseus's result to be erroneous. In all the demon- 

 strations sines are employed to the exclusion of chords. (Delambre.) 

 Upon the whole, this epitome is supposed to have been chiefly 

 extracted from the -Latin version which Gerard of Cremona had made 

 of the Arabic commentary of Geber on the ' Almagest.' It appears in 

 effect that both Purbach and Miiller rather divined the sense and 

 seized the spirit of Ptolemsous than understood the letter of their text. 

 The work was a model of precision; but nevertheless it was an abridg- 

 ment, and an abridgment of Geber much more than of Ptolemseus. 

 (Preface to the French translation of the 'Almagest,' by M. Halma, 4 to, 

 Paris, 1813.) 



After some years' residence at Vienna, Miiller was invited by the 

 king of Hungary (Matthias Corvin) to take up his abode at Buda, 

 where he amused himself with collating the Greek manuscripts which 

 had been brought from Athens and Constantinople, and in constructing 

 " tables of directions," in which he shows himself no less attached to 

 astrology than to astronomy. The work is entitled ' Tabula? Direc- 

 tionumProfectionumque, non tarn Astrologiae Judiciarise quamTabulis, 

 instrumentisque innumeris fabricandis utiles ac necessarise,' &c., 4to, 

 Niirnb., 1475. It contained the first tangents published in Europe, 

 extended however only to each degree of the quadrant ; but although 

 similar tables had been constructed by the Arabs, and applied by them 

 to trigonometry full 500 years earlier, Miiller, as has been stated, was 

 quite ignorant of this their chief use. The work is reviewed in the 

 ' Astr. du Moyen Age,' pp. 288-292. It may here be observed that the 

 term ' tangents' was not introduced till after the time of Miiller. Both 

 by him and Purbach, as by the Arabs, they were called ' shadows,' 

 the length of the shadow of every object cast by the sun being in fact 

 the tangent of the sun's zenith distance, the radius being the vertical 

 height of the object. The state of Hungary induced him in 1471 to 

 remove to Niirnberg, where he formed an intimacy with a wealthy 

 citizen, Bernard Walter, at whose expense several astronomical instru- 

 ments were constructed and a printing-office established. With these 

 instruments a series of observations were made which afforded abuc dant 

 proof of the inexactitude of the Alphonsine Tables. They were pub- 

 lished in 1544 iinder the title of ' Observationos 30 Annorum h, J. 

 Regiomontano et B. Walthero. Scripta de Torqueto, Astrolabio 

 Armillari, Regula magna Ptolemai'ca, Baculoque astronomico,' 4to, 

 Niirnb. Muller's observations commence at Rome the 3rd of January 

 1462, and at Niirnberg the 6th of March 1472, and terminate the 28th 

 of July 1475. Those of Walter begin the 2nd of August 1475, and 

 end the 3rd of June 1504. Lacaille made use of these observations in 

 the construction of his solar tables. ('Astr. du Moyen Age,' p. 337.) 

 The appearance of a comet led him to compose a work entitled 

 ' Problemata xvi. de Cometge longitudine, magnitudine, et loco vero,' 

 first published at Niirnberg in 1531, 4to, wherein he gives a method 

 of determining the parallax of a cornet, afterwards employed by Tycho 

 Brahe", but which, observes Delambre, though true in theory, cannot 

 be depended on in practice. ('Astr. du Moyen Age,' pp. 340-344.) 

 Prior to 1475 he published his 'Kalendarium Novum,' for the three 

 years 1475, 1494, and 1513 (the interval being an entire cycle of nine- 

 teen years), which was probably the first almanac that appeared in 



Europe, though the idea was taken from a similar work composed 

 by Theon of Alexandria. It gives the length of day at all places 

 situated between the parallels of 36 and 55 N. lat., and for every 

 three degrees of the sun's longitude. On the appearance of this 

 almanac the King of Hungary presented Miiller with 800 (some say 

 1200) crowns of gold; and such was the demand for it that, notwith- 

 standing the price of twelve gold crowns, the whole edition was speedily 

 disposed of in Hungary, Italy, France, and England. Besides the above 

 works of his own composition, ho had printed an edition of Purbach's 

 'Theory of the Planets,' the 'Poems' of Manillas', &c., and was pro- 

 ceeding with others, when Pope Sixtus IV., who contemplated a 

 reformation of the calendar, purchased his services by appointing him 

 Archbishop of Ratisbon. He immediately quitted his old patron 

 Walter, and proceeded to Rome in July 1475, where he died on the 

 6th of July of the following year, in the forty-first year of his age. 

 His body was interred in the Pantheon. 



Muller, observes Delambre, was a man of remarkable sagacity, and 

 of an ardent and enterprising disposition. He was without contradic- 

 tion the most learned astronomer that Europe had then produced ; 

 though he was inferior to Albategnius as an observer, and to Aboul 

 We"fa as a calculator. It is matter of astonishment that, having recog- 

 nised the advantage of employing tangents in some few particular 

 cases, he should not have seen the importance of introducing them, 

 into ordinary calculations. He had shown the inaccuracy of the Alphon- 

 sine Tables, had contemplated their improvement, and had instituted 

 a systematic course of observations for that purpose ; time and leisure 

 were alone wanting to the realisation of his views. His journey to 

 Rome and premature death occasioned an injury to astronomy which 

 it required a long interval to repair. 



The following list of his works, not already mentioned, is taken from 

 the list given by Delambre, in the ' Biog. Univers.,' compared with 

 that given by Niceron. With the exception of the first two, they 

 were all published after his death: 1, ' Disputationes contra Cremo- 

 nensia in planetarum theoricas deliramenta,' Niirnb., 1474, fol. 2, 

 ' Tabula magna primi mobilis,' Niirnb., 1475. 3, ' Almanach, ab anno 

 1489 ad annum 1506.' 4, ' In Ephemerides Commentarium,' Venice, 

 1513, 4to. 5, 'Tabulae Eclipsium Purbachii. Tabulae primi mobilis 

 a Monteregio,' Venice, 1515, fol. 6, ' Epistola de compositione et usu 

 cujusdam meteoroscopii armillaris,' Ingolstadt, 1533, fol. (appended to 

 an edition of Apian's ' Introduction to Geography '). 7, ' Problemata 

 29 Saphese nobillissimi instrument! a J. de Mouteregio,' Niirnb., 1534. 

 (The Saphee bore some resemblance to the Analemma.) 8, ' Maho- 

 metis Albategnii de Scieutia Stellarum Liber, Latine ex Arabico per 

 Platonem Tiburtinum versus, et additionibus aliquot Joannis Regio- 

 montani illustratus,' Niirnb., 1537, 4to (Niceron). 9, 'De Ponderibus 

 et aquseductibus, cum figurantibus Instrumentoruin ad eas res neces- 

 sarioruin,' Marpurgi, 1537, 4to. 10, ' Tabulae Revolutionum,' 4to, n. 

 d. 11, 'De Influentiis Stellarum,' Argeutorati, 1538. 12, 'Problemata 

 Astronomica ad Almagestum spectautia,' Niirnb. 1541 (Niceron). 13, 

 ' Fundamenta operationum qua) fiunt per tabulam generalem,' Idem., 

 1557, fol. 



Three manuscripts, in Muller's handwriting, came into De Murr's 

 possession. One consisted of notes on the Latin version of Ptolemaeus's 

 Geography. The second was his defence of Theon against Trebizond. 

 The third was entitled ' De Triangulis omnimodis Liber V.' Extracts 

 from these were published by De Murr, under the title of ' Noticia 

 trium Codicum autographorum Johannis Regiomontani,' Niirnb., 1801, 

 4to. Muller's Letters were also published by De Murr in 1786, in his 

 ' Memorabilia Bibliothecarum publicarum Norimbergensium et Uui- 

 versitatis Altdorfianfe,' tome i. pp. 74-205. See also ' Astron. du 

 Moyen Age,' pp. 344-65. Weidler, in his ' Historia Astronomise,' pp. 

 310-13, gives a list of the works which issued from Muller's press at 

 Niirnberg, and also of those which he contemplated publishing. 



(Montucla, Histoire des Mathematiques, and the works above quoted. 

 The reader may further consult the Life of Muller by Gassendi, 

 appended to his Life of Tycho BraM, Paris, 1654, 4to; Fabricius, 

 Bibliotheca Latina Medice et Infimce Latinitatis, torn, iv., p. 353; Pauli 

 Jovii Elogia, No. 144.) 



REGNARD, JEAN-FRANCOIS, was born at Paris, according to 

 most accounts, in 1647, though in a short biography prefixed to an 

 edition of his works (Paris, 1818, 4 vols. 18mo), he is said to have been 

 born in 1656. An only son and heir to considerable wealth, he received 

 an education qualified to fit him for the position in life he was likely 

 to occupy. The death of his father soon after he had completed hia 

 studies enabled him to gratify his desire for travelling. The first 

 country that he visited was Italy, where he spent the year 1676, a date 

 which, connected with other circumstances, renders it probable that 

 1656 was the real year of his birth. He revisited Italy a second time 

 in 1678, on which occasion he formed an intimacy with the Eloise, 

 whose memory he has consecrated in his pleasing little novel entitled 

 ' La Provengale,' a work published after his death. This lady and her 

 husband were induced by him to visit France, and for that purpose 

 they all sailed from Civita Vecchia in an English vessel bound for 

 Toulon. On the voyage however the vessel was captured by Algerine 

 pirates, and Reguard and his companions were taken captives to Algiers. 

 The adventures of their captivity form the basis of the novel above 

 mentioned, and they are sufficiently interesting and romantic in them- 

 selves without the colouring of fiction. The only talent of Regnard 



