A Valediction

To the Cultivator of Mathematics

Henry Gellibrand

As always untimely, and ruinous to the State of Knowledge shall be the death of those who prepare anything of lasting importance, would that any other instead of our most learned Briggs was having to suffer! ( for whom generations of Mathematicians plainly are filled with wonder.) Thus truly, neither would Posterity have been deprived of his light, nor with such labour would the burden have weighed upon my poor shoulders, nor of being caught unawares to such an extent by the imposition of this difference of web that had to be spun.

For the Author to be honoured amply with this most noble Epilogue, after having been engaged laboriously in a life of Mathematics, if this work should happen to finish off the incomplete; as the Graces¹ would not have failed to carry off this memorial itself to the gods. Scarcely indeed on another man, so completely did the burden with all his numbers fall on us as on Atlantus², for the Hero of Arithmetic and Geometry was becoming infirm. It had been for him to discover very clearly, to set forth with vigour, [and] to arrange neatly [the numbers which he had] so abundantly given, as may be confirmed from the first part of this work: as with the picture of Venus of Antiquity, when the untimely death of Apelles³ had left the work unfinished, no one who followed the prescription from the drawings had found himself able to complete the remainder; Much less for us after so many things of such greatness, we would appropriate the pencil for an eternity: but God governs [the lives] of all the wisest, Apelles was looked after, then our septuagenarian Author, with himself as it were, now being summoned away from the earth, [leaving] his work in the hallway.

Because even as long ago as thirty years, more or less, he had been able to complete accurately this Table of Sines, to fifteen places, through algebraic equations and differences, themselves proportional to Sines, being erected from the first fundamentals, and by earnestly continuing the association to the state of exhaustion; as for the Tables, an edition together with [chapters on] the construction and use was being considered, (which was scarcely permitted on account of the public affairs with which he was involved ) so much of the work being performed by hand with difficulty, as [he had been] a midwife by practise I may say⁴, with helping women in labour; as it were with the effort, [so] life finished together with the end of the first book, indeed not a vestige of the making of the following book being left after him.

And thus by the order of the Author now with the Blessed (while still alive, he was upright and reasonable about religion to me⁵ ), then with the encouragement of the most distinguished and eminent of men knowledgeable of mathematics: Master Christopher Gardiner, Haling, Bearer of Arms; Master John Welles, Deptford, Bearer of Arms; Master Richard Lever, London, Gentleman, and of others to whom I owe the most; and finally the most distinguished and learned of men, Master Adrian Vlacq, by request, who with his own printed Tables⁶ being brought out, from the first being prevailed upon, had been commissioned on account of the measure and fineness for our Tables [for which] I was accumulating examples [of their uses], from the outlines of Napier and Briggs, as far as I was able to follow.

Readers being earnestly entreated to be willing, concerning what the quality of these things of ours may be, to be interpreting clearly, and the errors which occur should be corrected (for I was not able to be present, with the printing being overseas ). Because if any of the Tables should be suspected to be in error, any changes to the numbers in the majority of cases will be able [to be done] by means of Differences. The Differences are not difficult to be investigated.

Farewell.
From Gresham College, before the day of the third Calends, November, from the year of deliverance, 1632.

¹ The three Graces were goddesses in Classical times.

² The author portrays himself as a poor substitute for a giant, barely able to support the load left on his shoulders by his friend Briggs.

³ A famous Greek painter, a contemporary of Alexander the Great, who lived on the island of Cos.

⁴ In 1588 (some sources give 1589) Briggs was elected a fellow of St John's College, Cambridge, and then, in 1592, he became:-
Reader of the Physic Lecture founded by Dr Linacre.
'Thomas Linacre, born almost exactly 100 years before Briggs, had been so upset by the fact that medicine was practiced by barbers and clergymen without proper qualifications that he founded the Royal College of Physicians of London. The Linacre lectureship that Briggs was appointed to was therefore a medical lectureship but, in the same year of 1592, Briggs was also appointed as an examiner and lecturer in mathematics at Cambridge. It certainly appears that his talents were wide ranging.'
[From the article on the life of Briggs by J J O'Connor and E F Robertson, on the School of Mathematics and Statistics, St Andrews University, web site on the history of Mathematics].

This early excursion by Briggs into the realms of medicine was obviously a source of some amusement to at least one of Briggs' mathematical contemporaries, though here it seems a little tasteless: though it indicates something of the banter and wit of Briggs' character. Briggs of course was not free to marry, as a Professor of Gresham College. We have to bear in mind that Gellibrand (1597 -1636) was still quite a young man of 35 years at the time of writing: sadly, he himself was to live for only a few more years.

⁵ Gellibrand had taken Holy Orders.

⁶ Vlacq, a publisher, with his associate de Decker, a schoolmaster and surveyor, had adapted Briggs' Arithmetica Logarithmica by completing the missing Chiliades, working to 10 decimal places instead of the 14 in the original, in which case the easier interpolation scheme of Chapter 12 could be used. Originally, de Decker had printed these tables off for himself in Dutch in 1627 at Gouda, under the title Tweede Deel Nievwe Tel-Konst ofte Wonderliicke Konstighe Tafel; most of the copies were destroyed, it appears, by Vlacq, who proceeded to publish his Latin version of Briggs' work, with the method of calculation of the logarithms and some applications. Unfortunately, he left out the all important chapters 12 and 13 on difference methods, and moved other section around in the book. Briggs was not overly impressed, as he records in this work: however, he had left the door open for such a development, as he had invited anyone to complete the missing Chiliades in the Preface to the Arithmetica, though he did not have the approach adopted by Vlacq in mind.