Limenheuretica [Greek], sive porluum investigandorum ratio. Metaphraste Hug. Grotio Batavo.

Leiden: Ex officina Plantiniana apud Christophorum Raphelengium. Academiae Lugduno-Batavae Typographum, 1599.

First Latin edition, extremely rare, of Stevin’s highly important work on the determination of position at sea using the magnetic variation (or declination) of the compass needle, the angle between magnetic north and true north; since latitude was simply measured, this was tantamount to the determination of longitude. Originally published in Dutch as De Havenvinding, “the [Latin] translation appeared almost simultaneously with the original Dutch version” (Crone et al., p. 375); English and French translations followed later in the same year. “In a seafaring nation like the Dutch republic matters of navigation were, of course, of great importance. In addition to his astronomical works, Stevin … approached the subject of determining the longitude of a ship, a problem that was not fully solved until the nineteenth century. Several previous authors had suggested that longitude might be determined by measuring the deviation of the magnetic needle from the astronomical meridian, a suggestion based on the assumption that the earth-wide distribution of terrestrial magnetism was known. Since the determination of latitude was well known, such a measurement would allow the sailor to chart longitudinal position against the latitudinal circle. Stevin, in his booklet, gave a clear explanation of this method; he differed from Petrus Plancius and Mercator in that he did not rely upon a priori conceptions of the way in which geomagnetic deviation depends upon geographical position. Although he was willing to offer a conjecture about this dependence, Stevin insisted on the necessity of collecting actual measurements from all possible sources and urged the establishment of an empirical, worldwide survey. His method was sound, although as data began to accumulate it became clear that the magnetic elements were subject to secular variation. The problem of determining longitude was at last solved more simply by the invention of the ship’s chronometer” (DSB). The Latin translation of De Havenvinding is important as the first edition to be published in a language understood throughout Europe, and hence is likely to have been much more widely read that the Dutch original. It also contains a fascinating dedication by Grotius, not of course present in the Dutch edition (or in the English and French editions). According to ABPC/RBH, in the last 50 years no copy of the Dutch or Latin editions has sold at auction; they list just the Macclesfield copy of the French edition, and the Streeter/Boies-Penrose copy of the English edition (sold Christie’s New York, April 16, 2007, $36,000). OCLC lists no copies in US.

“By the end of the sixteenth century the Dutch Republic had become a major sea power … It was thus understandable that the authorities in the Dutch Republic – Prince Maurice (1567-1625) and the States general – were greatly interested in a safe and speedy method of maritime travel. Maurice showed considerable enthusiasm for nautical affairs, and it is likely that he asked Stevin to prepare a study of the subject …

“Stevin explains what he intends right at the start of the book. ‘It is known,’ he says, ‘that for a long time past, principally since the great voyages to the Indies and America began, a means has been sought by which the navigator might know at sea the longitude of the place where his ship is at the moment in order thus to get to the harbours to which he wishes to go, but that hitherto it has not been possible to arrive at such accurate knowledge of the longitude. For some people, hoping to find it through the variation of the compass, ascribed a pole to the said variation, calling it magnetic pole, but it is found upon further experience that these variations do not obey a pole. Nevertheless the search for this has furnished a means for reaching a desired harbor, even though the true longitudes of both the harbor and the ship are unknown.’ In navigation, the ‘variation of the compass’ is understood as the angle between the geographic and magnetic meridian. Gerardus Mercator (1512-94) and Pieter Plaetevoet (1552-1622), known as Plancius, a Dranouter-born pastor of the Reformed Church in Amsterdam, had written on the phenomenon of magnetic variation before Stevin, and he had tried to make use of it in practical navigation and in attempts at determining longitude. Stevin’s aim was clearly much more modest: he sought to enable the seafarer to reach a given harbor without having recourse to longitude.

“Moreover, Stevin was not convinced of the existence of a magnetic pole, conceived as a rock located somewhere in the Arctic. In De Havenvinding he makes no attempt to explain the variation of the compass needle or terrestrial magnetism in general, as his predecessors Plancius and Mercator had done. But he did make a thorough study of the observational data Plancius had collected and expanded on them.

“Plancius assumed that there were four meridians on earth where the variation was zero: the prime meridian, which at that time passed over the island of Corvo in the Azores, and the meridians of 60°, 160° and 260° east longitude. In each of the four lunes into which these meridians divide the earth’s surface, the needle is supposed to deviate from magnetic north in the same way. That is northeasterly in the lunes I (0-60°) and III (160-260V), and northwesterly in the lunes II (60-160°) and IV (260-360°). The northeasterly variation would increase in lune I from 0° to 30° eastern longitude and decrease from 30° to 60° and so on. Stevin concurred with Plancius as regards lunes I and II, for which there existed sufficient observational data, but in place of four agonic lines [meridians of zero variation] he introduced six, at 0°, 60°, 160°, 180°, 240° and 340°, and cautiously presented his system as conjecture or supposition. Although Stevin criticized certain aspects of Plancius’s work and used his method in a more restrained form, he made no attempt to hide his admiration for his predecessor’s data gathering, ‘listing in a table the variations that have already been observed, which the learned geographer Mr Petrus Plancius has collected by protracted labour and not without great expense from different corners of the earth, both far and near, so that, if navigators shall find land and harbours generally in this way, as some in particular have already found them, the said Plancius may be considered one of the principal causes of this.’

“Stevin advocated the use of the tables of variation to find harbours or even to enable ships belonging to the same fleet to regroup at a specific point. He interpreted the proposition in an appendix to De Havenvinding thus: ‘Since the given variation and latitude in combination indicate a definite point, both at sea and on the land, it follows from this that it is possible for ships to find each other at a given point at sea, far from the land. This is useful, among other things, to help the ships of a fleet to reassemble after a storm. By this means it is also possible to fix a rendezvous where ships coming from different directions may meet at a predetermined time.’

“If this technique was to be truly reliable, the collection of compass variations at as many positions in the world as possible was essential. Prince Maurice ordered that navigators should henceforth ‘find out actually and very carefully the variations of the needle from the north’ and faithfully report the results of their observations to the Admiralty so practical tests could be made. Stevin studied the various methods of observing variations, finally recommending a way of measuring them in De Havenvinding. In a section entitled ‘How the True North and the Variation are Found’ he explains how observations can best be taken. The navigator should use ‘an azimuthal quadrant, the horizontal plane of which, notwithstanding the movement of the ship, always remains level.’ In the margin of the page, Stevin provides a Latin translation for the description of this instrument Quadrantem Azimuthalium seu verticulu cuius planu horizontale – an azimuthal quadrant that turns about a vertical axis over a horizontal graduated circle. This instrument was built by Reynier Pietersz, also known as Reynier Pieter van Twisch. An inhabitant of Hoorn (in the province of North Holland), Reynier Pietersz worked for the Hoorn ship owners. In 1598 he applied to the states of Holland and Westfresia for a subsidy for the building of two instruments. One of these was no doubt his azimuthal quadrant. On 13 March 1598, the States appointed a committee consisting of Scaliger, Snellius, Van Ceulen and Stevin, together with the deputies of Amsterdam, Rotterdam, Hoorn and Enkhuizen, to examine and test the instruments and report on them. The committee’s conclusions are not known, but the fact that Stevin recommended the instrument and explained how it should be used suggests that the committee deemed Reynier Pietersz’s device to be useful and usable. Certain sources even describe it as the ‘Golden Compass’” (Devreese & Berghe, pp. 96-99).

The azimuthal quadrant is shown in the full-page illustration on p. 19. A vertical quadrant turns about a vertical axis over a graduated circle. At a certain instant before noon, the alidade is directed towards the Sun, and the angle between the plane of the quadrant and the needle is read, say a°. After noon the measurement is repeated when the Sun has the same altitude again. If the angle is now b°, the declination is (a – b)/2, easterly if a > b, westerly if a < b. In this diagram, H is a weight used for stabilization. Tables of the latitude, longitude and declination at various locations on the globe are given on pp. 6 & 7.

The ‘Privilege’ with which the work opens states that the States General of the United Netherlands, by letters patent of 18 March 1599, granted to Christoffel van Raphelingen (1566-1600), printer at Leiden and a grandson of the famous Christoffel Plantijn (Christophe Plantin) at Antwerp, for a period of six years, the sole right of printing, publishing, and selling this book. We also read there that Van Raphelingen intended to publish the treatise not only in Dutch but in Latin, French, and other languages, but Van Raphelingen actually brought out only a Latin and a French edition in addition to the Dutch; the English translation, The Haven-finding Art or the way to find any Haven or place at sea, by the Latitude and Variation, by the great mathematician and nautical expert Edward Wright, was printed and published in London, also in 1599. The Latin edition has a dedicatory epistle dated 1 April 1599, and therefore probably appeared within days of the Dutch edition. The English translation had a dedicatory epistle by Wright dated 23 August 1599; it therefore probably appeared four or five months after the Dutch and Latin editions. The French translation, Le Trouve-Port, contains no dedicatory epistle, no preface to the reader, nor any other data from which the exact date of its publication might be inferred; even the identity of the translator is unknown. The Dutch edition was reprinted in the Wisconstighe gedachtenissen and the Latin edition in the Hypomnemata mathematica, both published in 1605-8; the French edition was included in Les Oeuvres Mathématiques, published by Albert Girard in 1634. The book’s rapid translation into several languages indicates just how great was the interest it aroused in seafaring nations. De Havenvinding is the only work by Stevin not to include his name as author on the title page, not even in the original Dutch publication. However, his authorship is mentioned in Grotius’s Latin translation and in the English version by Wright.

“The jurist Hugo Grotius (1583-1645), a figure famed in world history, at the age of 16 years had translated The Haven-Finding Art faithfully into elegant Latin … Grotius wrote for the booklet a dedicatory epistle, addressed to the Doge, the Senate, and the people of Venice, and dated Delft, 1st April 1599. This date shows that the translation appeared almost simultaneously with the original Dutch version. It is not merely on account of the courtesy of the wording that this dedication is worth reading. It also contains some personal impressions of the author. It drives Stevin's meaning home to the reader more clearly than he himself had done and it throws full light on the importance attached to Stevin’s work by the leader of the country, Lieutenant-Admiral Prince Maurice.

“Grotius relates that he had met the Venetian ambassador while accompanying the Dutch embassy sent to Paris. After making a polite comparison between Venice and the Republic he states he had resolved to dedicate a work to the Venetians. The favourable occasion which was worthy of them and which enabled him to add a contribution of his own – a reference to his dedicatory epistle – had now arisen. He was able to offer and recommend a booklet containing instructions given by the Prince to the commanders of the navy and to their boards, to be followed by them. The Lieutenant-Admiral himself had previously studied the subject.

“After a circumstantial discussion of the development of ancient navigation and the knowledge of the compass,' Grotius recalls how on voyages from east to west the compass-needle had been found to deviate gradually and not inconsiderably from the true north, which had caused great doubt and uncertainty among seamen. Thanks to prolonged observation of the magnetic declination at different times and places it had been found by the most learned mathematicians – as one of whom he considers Prince Maurice – that this was no mere accident, but that in nature a certain regularity (ratio et norma) existed according to which the pointings of the needle varied. The Prince had now presented these instructions, written about the matter by his mathematician Stevin, to those in authority in maritime affairs, in order that, if there should be found to exist disagreement between theory and personal observation, every effort might be made to deduce a rule from different experiments.

“In order that as many data as possible might be collected, the Prince had decided to present the booklet to the Doge, so that the Venetian navigators might take similar observations, which would make for greater certainty in the finding of any destination. Grotius concludes his dedicatory epistle with a general recommendation of the method and with the wish that “this small present” might be sympathetically received, “which will be of benefit to both parties and to the whole of the human race”. The high expectations that were entertained – by the Prince in particular – of the fruits of Stevin’s work could hardly be expressed more eloquently” (Crone et al, pp. 375-6).

One of the most original scientists of the sixteenth century, Simon Stevin (1548-1620) “was a merchant’s clerk in Antwerp for a time and eventually rose to become commissioner of public works and quartermaster general of the army under Prince Maurice of Nassau. He engineered a system of sluices to flood certain areas and drive off any enemy, an important defense of Holland. He also invented a 26-passenger carriage with sails for use along the seashore. In De Beghinselen der Weeghconst (1586; “Statics and Hydrostatics”) Stevin published the theorem of the triangle of forces. The knowledge of this triangle of forces, equivalent to the parallelogram diagram of forces, gave a new impetus to the study of statics, which had previously been founded on the theory of the lever. He also discovered that the downward pressure of a liquid is independent of the shape of its vessel and depends only on its height and base. In 1585 Stevin published a small pamphlet, La Thiende (“The Tenth”), in which he presented an elementary and thorough account of decimal fractions and their daily use. Although he did not invent decimal fractions and his notation was rather unwieldy, he established their use in day-to-day mathematics. He declared that the universal introduction of decimal coinage, measures, and weights would be only a question of time. Stevin published a report in 1586 on his experiment in which two lead spheres, one 10 times as heavy as the other, fell a distance of 30 feet in the same time. His report received little attention, though it preceded by three years Galileo’s first treatise concerning gravity and by 18 years Galileo’s theoretical work on falling bodies” (Britannica).

Bierens de Haan 4565; Dijksterhuis X and pp 87-92; Taylor, Mathematical Practitioners of Tudor and Stuart England, 99/100b; Waters, The Art of Navigation, pp. 229-230. Crone et al (eds.), The Principal Works of Simon Stevin, Vol. III, 1961. Devreese & Berghe, ‘Magic is no Magic’: The Wonderful World of Simon Stevin, 2008.

Small 4to (229 x 160mm), pp. [xii], 21, [1], with woodcut printer’s compass device on title and three woodcut illustrations in text, two full-page (a few minor spots and stains). Eighteenth-century gilt Buntpapier. A very good copy of an extremely rare book.

Item #5421

Price: $35,000.00