Whence Recorde infers that number "is the onelie thing (almost) that seperateth man from beastes. Hee therefore that shall contempne numbre, he declareth himselfe as brutishe as a beaste, and unworthy to be counted in the fellowshippe of men. But I truste there is man so foule ouerseene, though mainie right smallye do it regarde." Again, the work opens with a dialogue on the advantages of number, from which the following is an extract:

      "      Mayster. If Numbre were so vyle a thinge as you did esteeme it, then neede it not to bee used so muche in mens communication. Exclude Number and aunswere me to this question. How many yeares olde are you?
      "      Scholer. Mum.
      "      Mayster. How many daies in a weeke? how many weekes in a yeare? What landes hathe youre father? How many men dothe he keepe? Howe longe is it sythe you came from him to mee?
      "      Scholer.      Mum.
      "      Mayster. So that if Numbre wante, you aunswere all by Mummes : How many myle to London?
      "      Scholer. A poke full of Plummes.
      "      Mayster. Why, thus you may see, what rule numbre beareth / p.11 / and that if Numbre be lackinge, it maketh men dombe, so that to moste questions, they must aunswere Mum.
      "      Scholer. This is the cause Syr, that I judge it so vyle, bycause it is so common in talking euery while: For plenty is not deinty, as the common sayeng is.
      "      Mayster. No, nor Store is no sore: perceaue you this?" &c.

      The work contains numeration, addition, subtraction, multiplication, division, reduction, progression, the golden rule; a treatise on reckoning by counters, on a principle much resembling that of the Chinese abacus; a system of representing numbers by the hand, like the alphabet for the deaf and dumb; a repetition of all the rules for fractions, with the rules of Alligation, Fellowship, and Falsehood (false position). On the latter rule he remarks that he was in the habit of astonishing his friends by proposing difficult questions, and working the true result by taking the chance answer of "suche children or ydeotes as happened to be in the place."
      It may, perhaps, be a question whether this work was not published originally so far back as 1540; for when John Dee (in his edition) comes to the table of coins, he reminds the reader that the table was of coins such as they were when the author first published his book; after which he heads the table, "A table for Englishe Coynes. Anno 1540." It may not be amiss to give this list of coins, which we do in modern spelling:--
      Gold Coins. -- A sovereign was two royals, three angels, 4[half] crowns, or 22s. 6d.; half a sovereign, or a royal; the half-royal and the quarter-royal; an old / p.12 / noble, called a Henry, was two crowns; half an old noble; an angel was 7s. 6d.; half an angle; a George noble, 6s. 8d.; half a noble; a quarter of a noble, "which in the old statues is called a farthing;" a crown, or 5s.; a half-crown; another crown of 4s.6d., "known by the rose side, for the rose hath no crown over it."
      Silver Coins.-- The groat of 4d.; another groat, called a harp, of 3d.; the penny of twopence; the dandiprat of 1[half] d.; the penny, the halfpenny, and the farthing.
      The pound of 20s., the mark of 13s. 4d., and the shilling of 12d. were not coins, "yet there is no name more in use than they."
      Of the "Pathway to Knowledge" we have little to say. Probably the translations of Euclid drove it out of the market. It contains -- 1. A method of working the various questions of practical geometry; 2. A description, not a demonstration, of the theorems in the first four books of Euclid; the whole in a highly useful form.
      The "Castle of Knowledge" is a more remarkable work. It is dedicated in English to Queen Mary, and in Latin to Cardinal Pole. From the preface to the reader, we gather that Recorde had not abandoned astrology. It begins with an account of the Ptolemaic system. All that is cited from Euclid and Proclus is in Greek and Latin, usually both, and Linaker's edition of Proclus is referred to; but the edition of Euclid is not mentioned.

/ p.13 /

      In the "Pathway to Knowledge," we observe a strong tendency to turn all Greek names into Saxon-English*;

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   * Recorde, as Tanner observes, was skilled in the Saxon language, as appears from his notes in a MS. at Corpus Christi College, Cambridge. See Berkenhout's Biographia Literaria, p.422.
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but in the present work we find many such English renderings given, though the terms of Greek etymology are preferred. The meridian is called the noon-steede circle; the zodiac, the thwarte circle; a sphere is said to be a round and sound (perfectly enclosed) figure; the Pleiades (or seven stars) are called the brood hen; the belt of Orion, the golden yard; the milky way, Watling-street; antipodes are called counterfooted. The astonomical instruments in use are described with the following names:-- "The Astrolabe, the plaine sphere, the Saphey, the quadrante of diverse sorts, the Chylynder, Ptolome his rules, Hipparchus rules, Tunsteedes rules, the Albion, the Torquete, the Astronomers staffe, the Astronomers ringe, the Astronomers shippe, and a greate numbre more." We learn that these instruments were described in the "Gate of Knowledge."
      The "Whetstone of Wit" was dedicated to the "companie of venturers into Moscovia." After treating of numbers in general, with the formation of powers and rootes, he comes to the consideration of cossike numbers, meaning an indeterminate number expressed by a letter, as in what is now called algebra. But Recorde does not use this term except to / p.14 / denote the application of cossike numbers to the solution of equations, which he calls the rule of Algeber. In this treatise he appears to have compounded, for the first time, the rule for extracting the square roots of multinomial algebraic quantities, and also to have first used the sign = . In other respects he follows Scheubel, whom he cites, and Stifel, whom he does not cite. There is nothing on cubic equations, nor does he appear to have known anything of the Italian algebraists. But the subject of Recorde's algebra can only be discussed at length and in connexion with the rise of algebra in other countries. This is completely done in Dr. Hutton's tracts, vol. ii. It may be observed, however, that Recorde was one of the first who had a distinct perception of the difference between an algebraical operation and its numerical interpretation, to the extent of seeing that the one is independent of the other; and also he appears to have broken out of the consideration of integer numbers, to a much greater extent than his contemporaries. Pointing out to his pupil (for this work is also in dialogue) that a certain fraction appears to be absurd, as being "lesse than naughte," which the pupil admits, he then uses this phrase, "Yet maie your example serve, to teach and practise multiplication by, as well as any other. And furthermore, I will tell you by this occasion, that I spake to you, more after the opinion of the common nomber of artesmen, than after my owne judmente." He then goes on to show how the same expression ceases to be absurd when a fraction / p.15 / less than unity is the cossic number, and to distinguish generally between the powers of integers and fractions. In perception of general results, connected with the fundamental notation of algebra, Recorde shows himself superior to others, and even we may say, to Vieta; though of course immeasurably below the latter in the invention of means of expression. He (and Scheubel also) are free from the geometrical phantasms which haunted the inventor of the specious notation, and made him invest simple numbers with the character of planes, solids, &c.,and even imply that numerical equations were impossible unless their coefficients were thus considered. All his writings considered together, Recorde was no common man. It is evident that he did not write very freely at first in English, but his style improves as he goes on. His writings continued to the end of the century to be those in common use on the subjects in which he wrote, though we must gather this more from the adoption of ideas and notation than from absolute citation*.

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* See a very able and learned article in the "Companion to the British Almanac" for 1837, p.30-37, by Professor De Morgan, and to which, it will be seen, I am indebted for some of the preceding remarks on Recorde's publications. I beg also to refer to three articles of mine on early English scientific literature, in the fourth volume of the "Magazine of Popular Science."
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      How melancholy is it to reflect that so much genius and learning should have been subjected to the baneful influence of poverty and imprisonment ! That Recorde's pecuniary difficulties were great is not to / p.16 / be doubted, and he plainly alludes to them himself at the end of his "Whetstone:" --

      "      Mayster. Harke, what meaneth that hastie knockyng at the doore?
      "       Scholer. It is a messenger.
      "      Mayster. What is the message? Tel me in mine eare. Yea, sir, is that the mater? Then is there noe remedie, but that I must neglect all studies, and teaching, for to withstande those daungers. My fortune is not so good, to have quiete tyme to teache."

      I have so recently entered into the question of the introduction of the Copernican heliocentric theory into England*,

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   * Philosophical Magazine, June, 1840. One of the most important additions to the historical literature of Wales has recently been published in the Appendix to the First Report of the Deputy-Keeper of the Public Records, p.79-122, being a very able and elaborate report on the records of Wales and Chester, by William Henry Black, Esq.
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that I do not consider it necessary to make a repetition in this place. Suffice it to say, that, as far as we can judge, Recorde is the first person in this country who adopted the views of Copernicus.