In November 1576 the Pacification of Ghent saw the Low Countries unite in a revolt against Spanish rule. It provided a basis for peace between the Catholic and Protestant areas but this soon ran into considerable difficulties. In January 1579 the Union of Utrecht saw the formation of 'The Netherlands' which gave the Calvinists the monopoly on religion in Holland and Zeeland. Lansberge could now return to his homeland and, in March 1579 he left London and returned to Ghent. He was still a young man, only 17 years of age when he arrived back in Ghent, but over the following months he preached in a number of different Calvinist churches in the area. In 1580, despite his youth, he was appointed as a Calvinist minister in Antwerp. He was also charged by the Board of the Reformed Church of Ghent, to preach the new doctrine in the small towns of Exaerde and Saffelaere. However, in Saffelaere he had trouble with the bailiff, Gilles van Bastelaer, who wanted to prevent him from performing the duties of his ministry. He received a call to Mechelen, just north of Brussels, but preferred to remain in Antwerp. However, warfare returned to the country as Alessandro Farnese, regent of the Netherlands for Philip II of Spain, made a military move to regain control of the south of the Netherlands. He began the action in the middle of 1583 and in the first half of the following year, he had captured territory so that Antwerp was cut off from the sea. Ypres and Bruges surrendered and Farnese laid siege to Antwerp. The city held out for over a year, but in August 1585 they surrendered. The Catholic south now accepted Spanish rule while the north remained largely Calvinist and opposed to Spanish rule. Farnese allowed the Calvinists in Antwerp to leave peacefully after the siege and move to the north and this is what Lansberge did, moving to Leiden.
In Leiden, Lansberge matriculated at the university and continued his studies of theology. After a year in Leiden, during which time he was influenced by the humanist thinkers there, he was appointed on 1 October 1586 to be a minister in Goes, in the province of Zealand. He had chosen to go to Goes after being given a choice between being a minister in that city or in Amersfort. Although he was now a minister with all the duties that entailed, nevertheless he spent much of his efforts working on mathematics and astronomy. He had clearly read Thomas Fincke's Geometriae rotundi (1583) for when he published his first book in 1591, Triangulorum geometriae libri IV, the influence of Fincke's important work is evident. Before we describe the contents of Lansberge's treatise, we note that his interest in astronomy, probably stimulated during his short stay in Leiden, led him to be dissatisfied with both Ptolemy and Copernicus. He believed that only through accurate astronomical observations could one build a satisfactory theory of the universe, and consequently by 1588 he was already making his own astronomical observations. We return later to describe his important contributions to the heliocentric theory, but first let us say a little about the mathematics treatise Triangulorum geometriae libri IV. As the title indicates, this consisted of four books. In the first book he gave definitions of the various trigonometric functions. The second book consists of a :-
... method of constructing the tables of sines, tangents, and secants, largely derived from those of Viète and Fincke, and the tables themselves, which were used by Kepler in his calculations.The third book is devoted to the study of plane triangles while the fourth, and final, book begins with a study of spherical geometry before giving a thorough look at spherical trigonometry. The book is not particularly original but has some things which lift it above similar texts from that time :-
In the solution of spherical triangles Van Lansberge employs a device similar to that of Maurice 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 (in Book IV) 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 Clavius.By the time this work was published, Lansberge had been married to Sara Lievaerts for a number of years and their first few children had been born. In total they had six sons and four daughters but not all their children reached adulthood. Their eldest son named Philippus, became a preacher in Kloetinge and died there in 1647. Pieter (born 1587) followed his father into the ministry, becoming a minister in Goes where he assisted his father. Jacob (born about 1590) made a career in medicine, becoming a medical doctor in Goes. He was also a fine mathematician and, following his father's death, defended the heliocentric views of his father against vigorous attacks.
In 1594 Lansberge published the well-respected religious work Catechesis religionis Christianae, quae in Belgii et Palatinatiis ecclesiis docetur, sermonibus LII explicata. This collection of 52 sermons on the Calvinist catechism, dedicated to the States of Zeeland, was written in Latin. It was published in Middelburg in 1594 and Neustadt in 1595, then reprinted in Hanau in 1620 and Frankfurt in 1621. A Dutch translation by S Ghys was published in 1645. In 1597 there was an attempt to call Lansberge to be a minister in Amsterdam. However, there arose a dispute between the town authorities and the church authorities over his appointment. The Leiden theologian Johannes Kuchlinus wrote to the burgomaster of Amsterdam warning him that Lansberge was more dedicated to astronomy than to his ministry:-
You have Plancius as a geometer, perhaps you will receive an astronomer: think it over whether such a ministry will be useful for your church. For the nature of astronomy is such that it induces the whole man to love it and indulge in deep speculation. He who takes care of many things, can give less attention to each separate thing.In the end, despite the attempts of the church to call Lansberge to Amsterdam, the town authorities refused to sanction the appointment and Lansberge remained in Goes. This certainly did not displease him for he was happy to be in that town. However by 1609 the political situation had changed making his position in Goes less secure. Goes was :-
... quite close to the frontier with the Spanish. It was a position which called for a militant attitude, and Lansberge certainly did not compromise. His implacability brought him into conflict with the local magistrate, who, especially since the Spanish menace had diminished since the truce of 1609, saw less need for such an attitude. Lansberge thought himself entitled to tell the magistrate how to act. A vigorous attack on the leniency of the town government of Goes, which allowed people suspected of Catholic sympathies to stand for the magistracy, eventually led to Lansberge's downfall.In fact, by 1610 both Lansberge and his son Pieter were ministers in Goes and both were dismissed in 1613. Lansberge accepted that his time in Goes was over and moved to Middelburg where he spent the rest of his life. However, his son Pieter did not accept the decision to dismiss him and, with the support of many from his church, appealed against it to the synod in 1618. He argued strongly that the action taken against both him and his father was unfair, but he failed to get the judgment reversed. In Middelburg, Lansberge used his skill in medicine as well as publishing books on astronomy and continuing to make astronomical observations.
In 1616 Lansberge wrote on π calculating it to 28 places using a new method. He presented his results in Cyclometria nova :-
He carried the value of 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.Lansberge's work on astronomy followed Copernicus's heliocentric theory although he did not seem satisfied with what Copernicus had presented. He wrote works supporting his own version of the heliocentric theory in both 1619 and 1629. The first of these, Progymnasmatum astronomiae restitutae de motu solis, was written to explain his attempt to present theories based on observations of both the ancients and his own. At first he had been unable to get the data to fit any theory but eventually he felt that he had succeeded. He wrote (see, for example ):-
I obtained the theory of the motions of sun and moon, as of the fixed stars, restored to their original state, so that they accord with the heavens, not only for this, but also for former centuries, up to 2000 years back.The 1619 book was the first of three intended volumes. It gave Lansberge's theory of the sun, presented with many tables to allow calculation of the sun's position at any time and in any place on earth. The promised second and third volumes, on the theory of the moon and on the precession of the equinoxes respectively, never appeared in print. Perhaps the fact that there was little reaction to this first volume dampened his enthusiasm to complete the project. However, when he was joined by an enthusiastic young astronomer Maarten van der Hove (who is better known by the Latin version of his name, Martinus Hortensius) in 1628, he quickly started publishing again. He wrote about Hortensius saying that he was fortunate:-
... that, by divine providence, in my old age, pressed by sickness, such a strong helper came to my aid, as formerly the learned Rheticus to the great Copernicus.Helped by his young assistant, Lansberge published in 1628 a second edition of his 1619 work, a manual on the use of the astrolabe and the quadrant, then, in the following year, he published a popular account of his heliocentric theories in Dutch under the title Bedenckingen op den dagelyckshen, ende jaerlyckschen loop van den aerdt-kloot. Hortensius translated this text into Latin and published it under the title Commentationes in motum terrae diurnum, et annuum (1630). The Dutch edition, written for those without mathematical skills, made quite an impact in Holland while the Latin translation was widely read and this soon led to Lansberge being strongly attacked by those opposed to the heliocentric theory. Of course, as a devout Christian, Lansberge had to explain why he was putting forward a theory which, apparently, contradicted the Bible. He wrote that St Paul, in his second letter to Timothy, says that Holy Scripture:-
... is profitable for doctrine, for reproof, for correction, for instruction in righteousness.However, Lansberge writes:-
... it is not intended for instruction in geometry and astronomy.The Bedenckingen contains many arguments intended to show that the heliocentric theory was correct. Many were not, one would have to say, very convincing and several scientists who believed in Copernicus's theories, for example Ismael Boulliau, did not accept Lansberge's arguments 'proving' that the heliocentric theory was correct. Among those who attacked Lansberge's work, one of the most vigorous of the anti-Copernicans was Jean-Baptiste Morin. It was left to Lansberge's son Jacob to reply to Morin and others in Apologia pro commentationibus Philippi Lansbergii in motum Terra, in which Jacob defended his late father's views.
Often when considering scientists from the seventeenth century, we look at their achievements and tend to ignore the world of magic and alchemy they inherited. Perhaps it would be fitting to look at the highly non-scientific world-view that Lansberge puts forward in the Bedenckingen clearly attempting to integrate the religious views of his day into his Copernican system. As was current at the time, he believed in "three heavens", but he adapted it to his heliocentric view :-
... the first heaven is that of the planets; it stretches from the sun in the centre up to the orb of Saturn. The second heaven is that of the fixed stars; it stretches from the orb of Saturn up to the eighth sphere, that of the fixed stars. The third heaven is the empyreal heaven, the throne of God and the place reserved for the Elect. This heaven is invisible to us, but we know about it from spiritual revelation. ... The immense space of the second heaven is not empty. It is full of 'a host of invisible creatures'. Angels descend from the third to the first heaven, or return in the inverse direction. Good and evil spirits engage in combat. Moreover, the two inner heavens can only function because of the force [from the Spirit of God] they receive from the third heaven.Now although Lansberge believed in a heliocentric system, he did not accept Kepler's ellipse theories and he published astronomical tables, based on circular orbits with epicycles, which he hoped would support Copernicus over Kepler. In 1632, the year of his death, Lansberge published Tabula motuum caelestium perpetuae, the astronomical tables that he had been working on for 45 years. There were three different parts to this work. One part was entitled "Perpetual tables of the heavenly motions, made up from, and in accordance with, the observations of all times". The second part gave the theory which he had developed to calculate his tables in the first part and was entitled "New and genuine theories of the heavenly motions". The third part, "A treasure of astronomical observations", collected a large amount of data on eclipses and similar events which had been recorded over the years. The quality of Lansberge's tables, published five years after Kepler's Rudolphine Tables, were not immediately obvious at first. Many accepted that the later tables by Lansberge would necessarily be more accurate than Kepler's and for around ten years this belief continued. However, defects began to show up and soon even his most enthusiastic supporter had turned against the tables.
Despite the weaknesses in Lansberge's work, he still deserves much credit for bringing the ideas of Copernicus to a wide range of people who did not possess the mathematical background to read advanced texts. The discussions and controversies that his work provoked were beneficial to the progress of science.
Article by: J J O'Connor and E F Robertson
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