Lansberge, Philip van

b. Ghent, Belgium, 25 August 1561; d. Middelburg, Netherlands, 8 December 1632),

geometry, astronomy.

On account of the religious troubles of those days his parents Daniel van Lansberge, lord of Meulebeke, and Pauline van den Honingh found themselves obliged to go to France in 1566 and afterward to England, where Philip studied mathematics and theology. He was already back in Belgium in 1579, where he received a call to be a Protestant minister in Antwerp in 1580. After the conquest of Antwerp by Spain on 16 August 1585, Philip left Belgium definitively to establish himself in to Netherlands. He went to Leiden, where he enrolled as a theological student. From 1586 to 1613 he was a Protestant minister at Goes in Zeeland, after which he went to Middelburg, where he died in 1632.

The Danish mathematician Thomas Finck had published an important work, the Geometriae rotundi, in Basel in 1583. It is this work that Van Lansberge seems to have followed very closely in his first mathematical study, Triangulorum geometriae libri IV of 1591. The first book is devoted to the definitions of the trigonometric functions. Van Lansberge, following Maurice Bressieu, used the term “radius” instead of “sinus touts.” The second book contains the method of constructing the tables of sines, tangents, and secants, largely derived from those of Viète and Finck, and the tables themselves, which were used by Kepler in his calculations. The third book is devoted to the solution of plane triangles and is accompanied by numerical illustrations. Van Lansberge’s statement and proof of the sine law differs very little from that given by Regiomontanus. The fourth book deals with spherical trigonometry; the first eleven items concern spherical geometry. In the solution of spherical triangles Van Lansberge employs a device similar to that of Bressieu in his Metrices astronomicae (Paris, 1581), the marking of the given parts of a triangle by two strokes. Van Lansberge’s new proof for the cosine theorem for sides (Book IV, item 17) marks the first time that the theorem appeared in print for angles as well as sides. But although Van Lansberge may lay claim to the discovery of the theorem for angles, sufficient evidence indicates that this theorem was known to Viète and to Tycho Brahe. On the whole Van Lansberge shows little originality in the content of his trigonometry, but his arrangement of definitions and propositions is less complicated and more systematic than that of Viète and Clavis.

In 1616 Van Lansberge published his Cyclometriae novae libri II, which was attacked the same year by Alexander Anderson in his Vindiciae Archimedis, sive elenchus cyclometriae norae a Philippo Lansbergio nuper editae. In this book Van Lansberge occupied himself with approximating the ratio between the circumference (Book I), the area (Book II), and the diameter of the circle. He carried the value of π to 28 decimal places by means of a method in which he seems to have joined the quadratrix of the ancients to trigonometric considerations. He thought that he had found a better approximation than that of Ludolf van Ceulen, who had used the Archimedean method of inscribed and circumscribed polygons and had carried the value of π to thirty–five decimal places in 1615. In his Progymnasmatum astronomiae restitutae de motu solis (Middelburg, 1619) Van Lansberge taught the probability of the earth’s motion according to the Copernican doctrine; the same is true of Bedenckingen op den dagelyckshen, ende jaerlyckschen loop van den aerdt–kloot (Middelburg, 1629), translated into Latin by M.Hortensius as Commentationes in motum terrae diurnum, et annuum (Middelburg, 1630). Both works were attacked for their Copernican ideas by Morin in his Famosi et antiqui problematis de telluris motu vel… (Paris, 1631), and by Libert Froidmond in his Anti–Aristarchs sive orbis–terrae immobilis; liber I (Antwerp, 1631). Although a follower of Copernicus, Van Lansberge did not accept the planetary theories of Kepler altogether. His Tabulae motuum coelestium perpetuae (Middelburg, 1632), founded on an epicyclic theory, were much used among astronomers, although they were very inferior to Kepler’s Rudolphine tables.

BIBLIOGRAPHY

I. Original Works. Van Lansberge’s works were published as Philippi Lansbergii Astronomi Celebrium Opera Omnia (Middelburg, 1663).

II. Secondary Literature, A very good biography is by C. de Waard in Nieuw Nederlandsch biografisch woordenboek (Leiden, 1912), cols. 775-782. Se also the following (listed chronologically): J. E. Montucla, Histoire des mathématiques, II (Paris, 1790), 334; D. Bierens de Haan, “Notice sur quelques quadraterus du cercle dans les PaysBas,” in Bullettino di bibliografia e di storia della scienze matematiche e fisiche,7 (1874), 120, 121; A. J. van der Aa, Biographisch woordenboek der Nederlanden, XI (Haarlem, 1876), 154-157; D. Bierens de Haan, “Bibliographie néerlandaise,” in Bullettino di bibliografia e di storia della scienze matematiche e fisiche,15 (1882), 229-231; A. Von Braunmühl, Vorlesungen über Geschichte der Trigonometrie, I (Leipzig, 1900), 175, 176, 192; C. de Waard, “Nog twee brieven van Phillips Lansbergen,” in Archief vroegere en latere mededelingen hellip in Middelburg (1915), 93-99; H. Bosmans, “Philips Lansbergens, de Gand, 1561– 1632,” in Mathésis; recueil mathématique,42 (1928), 5-10; C. de Waard, ed., Correspondance du M. Mersenne, II (Paris, 1937), 36, 511-513; and M. C. Zeller, The Development of Trigonometry From Regiomontanus to Pitiscus (Ann Arbor., Mich., 1946), 87, 94-97.

H. L. L. Busard