# A collection of letters illustrative of the progress of science in England, from the reign of Queen Elizabeth to that of Charles the Second/Preface

PREFACE.
The contents of the present volume are so very miscellaneous, that it would be a difficult task to give a satisfactory analysis of them within the limits of a few pages. Perhaps it may be sufficient to state that the Editor has endeavoured to form such a collection of early letters on scientific subjects as would be likely to assist any future author of a critical history of English science, and that from the very limited number of such letters which now remain he has attempted a selection which he thinks will be considered a valuable addition to the few materials of this class already published. The libraries of the British Museum, Sion College, Lambeth, and Oxford have been found to contain documents suitable for this purpose, and the reader will find that the following volume includes letters from all these depositaries.
To the cursory reader any illustration of the progress of science in this country during the reign of Elizabeth will be a novelty; and even those who have paid more particular attention to the subject will, we think, be surprised to find scientific correspondence ​of so early a date still preserved. Thanks to the venerable Lord Burghley, a few fragments are still preserved, which, though often individually of no great importance, are very curious illustrations of the state of English science at that period. For instance, the letter of Emery Molineux to Lord Burghley, printed at p. 37, is in itself of little interest or value; but when joined with the fact that it is the only known memorial respecting one who was distinguished as the first mathematical instrument-maker of his day, it becomes a document at once curious and valuable, and well worthy of preservation in an available form.
Before the publication of a very able and interesting paper on the early English mathematical and astronomical writers in the Companion to the British Almanac for 1837, written by Professor De Morgan, nothing had been attempted towards even a connected sketch of the scientific labours of our countrymen during the latter half of the sixteenth century. "Far from having," says Professor De Morgan, "such a work as those of Montucla or Delambre in our language, we have not even a chronological compendium like that of Weidler, Heilbronner, or Gerard Vossius." But necessarily imperfect in its details as Prof. de Morgan's sketch is, yet it may fairly rank with its continental companions, and gives, we may safely say, a ​correct and impartial account of almost every work that holds any importance either among the discoveries or mere elementary assistances of science. If we add to this, three articles in the Magazine of Popular Science, by the Editor of this volume, we shall have enumerated, we believe, every published contribution to the subject. It may, however, be mentioned, that Mr. Hunter discovered that John Field and John Dee adopted the Copernican system as early as 1556; and Professor De Morgan has shown that Robert Recorde was a convert to the heliocentric theory at nearly the same period. But these discoveries seem to have attracted little attention from scientific men, either on account of that lamentable apathy towards matters of history which is too frequently characteristic of the lover of demonstration, or perhaps, let us hope, from a want of some general channel of communication, such as the Historical Society of Science now affords.
The letters of Sir Charles Cavendish, which are, with two or three exceptions, now published for the first time, will, we think, enable the reader to form a tolerably correct idea of the extent to which the study of analytical science was then carried in England. If we give a glance at the state of this branch of science a short time anterior to that period, we shall be rather at a loss to account for the number and success of its English cultivators, who seem to have arisen on a sudden and at the same time with efforts sufficient to produce works equalling, if not surpassing, those of their continental neighbours.
​Robert Recorde may be considered as the founder of analytical science in England. The author of the first English work on algebra (1557) has not, however, as might have been expected, produced a mere elementary compilation, but a work that ranks, for originality and depth, with the ablest foreign contemporary productions on the same subject. What is rather inexplicable, this book by Recorde appears an oasis in a century deficient in this science, and no Englishman is known to have pursued the study of algebra to an equal extent before the time of Harriot. With the exception of a trifling essay by Thomas Digges in the Stratioticos, and a few memoranda in a MS. of Blagrave's in Lambeth Palace, we scarcely know of anything connected with this branch of science that is worthy of notice, and even these include only the simplest elementary principles.
It is somewhat remarkable that this dearth of analytical science was not the result of a prejudice in favour of the geometry of the ancients. We have, it is true, an elaborate edition of Euclid by Dee and Billingsley, but with this the taste for geometry appears to have expired. We do not find that Harriot and the contemporary English analysts were fettered by a prejudice in favour of the old geometry, such as for a length of time pervaded the writers of the continent; although, indeed, it appears from Harriot's ​papers in the British Museum that he was well acquainted with Pappus and other geometrical works which had then been recently published abroad. There is a remarkable note of Sir Charles Cavendish at p. 84, who says, "Dr. Jungius prefers the analitics of the ancients before Vieta's by letters, which he saies is more subject to errors or mistakes, though more facile and quick of dispatch, but I conceive not yet whye." This serves to show that the τοπος αναλυομενος of the Alexandrian school still held its sway in the minds of foreign mathematicians, notwithstanding the writings of Vieta and Descartes; but we find no traces in this country of its influence over the new analysis before the time of Robert Simson, that is, nearly a century afterwards.
The science of the seventeenth century possessed one feature which is now obsolete, and which probably contributed, in a great measure, to preserve and foster a taste for analytics. We allude to the practice of publicly proposing problems for solution—a kind of challenge from individuals to the science of all Europe—and thus exciting an emulation which, perhaps, would otherwise not have been felt. The superiority of the new analysis over the ancient geometry was soon acknowledged, and although some questions were required to be solved geometrically, yet mathematicians soon evinced their dislike to a system of attaining by a long and tedious method that which was often capable of speedy and easy resolution by another analysis. Specimens of these challenges are preserved among Pell's papers in the ​British Museum, printed on narrow slips of paper, and evidently intended to be pasted pro bono publico in conspicuous situations. We have little doubt that the celebrated problem, generally known as Colonel Titus's problem, was originally proposed in this manner. We have already intimated that this problem is attributed to the wrong person, and we have since discovered a note in MS. Birch, 4411, which expressly states that it was "put by Colonel Titus, who had received it from Dr. Pell." The problem in the most general form is as follows:
    $a^{2}+bc=\alpha$ $(1)$ $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$   $b^{2}+ac=\beta$ $(2)$ to find $a$, $b$, and $c$. $c^{2}+ab=\gamma$ $(3)$
Collins has given a solution which occupies fourteen closely written folio pages, and the more modern solutions have not been comprised in a much shorter compass. Wallis's solution is in the same manuscript. Pell, however, criticises Collins's solution very severely, and ridicules him for not observing that the roots will admit both of positive and negative values.
The problem is generally given with numerical values for $\alpha$, $\beta$, and $\gamma$, and the only possible chance of a short solution is a case in which these numbers bear some definite relation to each other, so as to obtain an equation independent of the given quantities. For instance, Pell gives one wherein $\alpha =15$, $\beta =16$, ​$\gamma =17$, in which case the problem remains in the same position as before with regard to a solution; but it is singular that Pell's ingenuity should not have suggested another method of solution in the case which he gives where $\alpha =7$, $\beta =7$, $\gamma =11$. In this case we have
    ${\begin{aligned}a^{2}+bc=b^{2}&+ac\\a^{2}-b^{2}=ac&-bc=c(a-b)\\{\text{or, }}&a+b=c\end{aligned}}$
It is unnecessary to pursue this any further, for by substituting this value of $c$ in $(3)$ and $(2)$, and adding the two equations together, we obtain $2(a+b)^{2}=18$, or $c=3$. The values of $a$ and $b$ are $1$ and $2$ respectively, and this is, perhaps, the simplest case which could be selected.
To return to the contents of our volume. The notes of inventions of Ralph Rabbards at p. 7, may be noticed as somewhat similar to the far-famed "Century of Inventions" of the Marquis of Worcester. The number of such proposals is great, and several seem to include discoveries generally considered as belonging to a more modern period. The letter of Tycho Brahe, at p. 32, may be mentioned as a curious notice of the intercourse between the mathematicians of this and foreign countries. The letters of Thomas Lydyat are more valuable for ​biography than the history of science; and yet we think that they will be acceptable to the lover of familiar history. Similar remarks may be made of others.
In the appendix to Dr. Vaughan's "Protectorate of Oliver Cromwell" are printed several letters from Pell's MS. collections, a few of which we have found it necessary to reprint in this work. Unfortunately no references whatever are given to the places whence these letters are taken, and amidst the very numerous volumes which compose Pell's collections, it is no easy matter to find the deposit of any particular one. Owing to this arrangement, we have been quite unable, although we have spared no exertions, to find the original of a very curious letter which Dr. Vaughan has printed at p. 347. It is written by Dr. Pell, and dated Oct. 12th, 1642; and we are unwilling to neglect the opportunity of extracting the following passage:—
"I can hear of nothing of Vieta's in manuscript in England, but such pieces of his as are already printed, and were transcribed for the most part out of the printed books, because they could not be had for money. Here is also a manuscript of his notæ priores ad logisticen speciosam transcribed many years ago at Paris out of a written copy; but since that time, le Sieur de Beaugrand hath caused it to be printed in 24mo. at Paris,anno 1631, with a few notes of his own thereon. It ​is true I have in mine own hands an imperfect astronomical manuscript of six sheets of paper, entitled Hypothesis Francelidinis, said to be a piece of a great work of Vieta's, called by him Harmonicum Celeste, which may, perhaps, be found complete in France, whence mine came. I have been told here that the Englishman that, at the time of Vieta's death, served him as a scribe, under the counterfeit name of John Poltrier, being kindly offered by Vieta's heirs to take what he pleased to keep as a remembrance of him, took not a leaf of any of his writings. And Thuanus tells us that the heirs did put all his papers in the hands of Peter Alelmus of Orleans. I never enquired whether this Peter were the father to Jacobus Alelmus, the French king's engineer; from whom, fourteen years after Vieta's death, Alexander Anderson acknowledgeth that he had those two tracts, de æquationum recognitione et emendatione, which he first published at Paris, anno 1615. And though it is likely that Monsieur Aleaume (for so I think the French call him) be now dead, yet I hope a diligent enquirer may learn who was his heir, and what is become of Vieta's Adversaria."
We consider this a most important testimony in favour of Nathaniel Torporley, who, according to Anthony à Wood, attacked Vieta under the name of Poultry. We now see the truth through Wood's mistake,—a mistake that has puzzled Professor Rigaud and other writers on the scientific history of this period. Perhaps Poltrier may be a mistake for Poltroyer, and intended for an anagram of the name of Torporley. This letter is also curious for the mention of Vieta's Harmonicon Cœleste, which has been but recently discovered, and is now in the course of publication at Paris by M. Libri.
We cannot conclude these few memoranda without offering our respectful thanks to His Grace the Archbishop of Canterbury, who, with the greatest liberality, has afforded us every facility for consulting the manuscripts in the library at Lambeth Palace.
J. O. HALLIWELL.
35, Alfred Place, Jan. 15, 1841.
* ↑ Davis, in the Seaman's Secrets, 4to. Lond. 1594, bestows the like praise upon him. According to Maunsel's Catalogue he was the author of a treatise on the use of the globes, but I have never been fortunate enough to meet with a copy.
* ↑ This is No. 280, which is classed anonymously in the printed catalogue. Blagrave has given in this volume the well-known algebraic question relating to the cocks of a cistern, besides several astronomical notes. It appears that Blagrave studied under John Field, whom we have mentioned above.
* ↑ Life of Sir Samuel Morland, p. 28.—" From No. 4413, fol. 24, it appears that the problem generally ascribed to Colonel Titus was proposed to Pell in 1649 by William Brereton, who very probably had it from Harriot."
* ↑ For instance, Sir Samuel Morland's Tuba Stentorophonica may have been anticipated by Henry Reginald, who, in the year 1603, dedicated a book of inventions to King James, among which was one "to convey the voice for a thousand paces without showing any one near you were talking."—MS. Birch, 4384.
* ↑ We have neglected to say in the proper place (p. 31), that "a copie of the speache made by the mathematicall lecturer unto the worshipfull company present, at the house of the worshipfull Mr. Thomas Smith," was published at London in 1588, small 4to. From the title-page to his treatise on the Cross-staf, it appears that Hood was mathematical lecturer in 1596; but in his work on the Sector, published in 1598, this title is omitted. We also omitted to remark, that from MS. Harl. 7523. fol. 206, it appears that Pell in 1650 had a design of publishing commentaries on the works of Descartes.
This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.
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