It gives also the_golden number, the epact, and the dominical letter. It may appear long, but it is broken up into the smallest subdivisions.

(b) Divide the given year by 4)1836

4)1851

4, and keep the quotient only; reject the remainder.

2294

2312

7)2312

rem. 5.

rem. 2.

(f) Divide (e) by 7, keeping 7)2294

the remainder only.

(g) Subtract (f) from 7; and the dominical letter is under the remainder below.

1 2 3 4 5 6 7 ABCDEFG

(h) Divide (a) by 19, the remainder is the golden number, or 19 is the golden number if the remainder be 0.

This gives nothing till

(i) From the number of centuries in the given year subtract 17, divide by 25, and keep the quotient A.D. 4200. only.

fited by it. For as long as he lived, he would neither return nor copy it; and I suspect he meant to pass it as his own." We now come to a curious specimen of the way in which a sentence is handed down by compilation from generation to generation. Edward Sherburne, in the notes to his translation of Manilius, London 1675, writes as follows: "But the work of his chiefly pertinent to our subject, and [whose loss cannot be sufficiently deplored, was his Harmonicon Cœleste, which, being communicated to Mersennus, was by some perfidious acquaintance of that honest-minded person, surreptitiously taken from him, and irrecoverably lost or suppressed, to the unspeakable detriment of the lettered world.] Vide Bulliald. &c. The learned Golius had it, and Sir Alexander Hume from hence imparted another copy; both which, 'tis feared, are lost, there being no impression made thereof; and Golius being since dead, his collections (whereof he had many in Arabick) are said to be dispersed, and (which is to be pitied) carried back by a Jew into Turkey." Benjamin Martin, in his Biographia Philosophica, 1764, repeats the clause in brackets; and Dr. Hutton, in his Mathematical Dictionary, 1815, does the same, substituting only "great" for "unspeakable," and literary" for "lettered." The assertion about Golius

66

*Iste; there is such confusion about this sentence, that we quote it entire; " Hic vir optimus et facilis à quodam viro non bonæ fidei illo libro emunctus est, ita ut nec ipsum Puteano reddere potuerit, nec respub. literaria fructum aliquem ex eo capere. Quamdiu enim vixit, iste nec reddere voluit nec copiam illius facere; et, nisi fallor, meditabatur sibi adrogare Vietæ hoc opus, veri authoris nomine suppresso." From the first clause in italics, we should suppose Bouillaud did not know who it was took the book (though quidam is there ambiguous); from the second, that he did know. And what we have presently to say makes this whole assertion still more inexplicable. Both Mersenue and Puteanus were alive when this was written P. Puteanus and Bouillaud were not only known to each other, but were, as long after the publication of the Ast. Philol. as 1679, engaged in a joint production (the catalogue of the library of Vieta's friend, the president De Thou.)

:

and Sir A. Hume, has some reference to the preface of Vieta's collected works by Schooten, published in 1646, in which it is stated that the editor had a copy of the Harmonicon, but not sufficiently complete to publish; but that he had received another copy from Alexander Hume, which would appear in a subsequent work, together with anecdotes (avékdoтa) of Vieta. No such work, however, was ever published.

This question being already sufficiently obscure, the writer of this article, some years ago, requested the late distinguished and excellent mathematician M.

to

make some inquiry upon the subject at Paris; and that gentleman soon found a circumstance which makes Bouillaud's assertion most singular: for, in the manuscripts of this very Bouillaud, he states that he, Bouillaud, had had the manuscript,* and had lent it, in 1662, to Prince Leopold of Tuscany, the protector of the Accademia del Cimento; from which the gentleman alluded to supposed that it might be now at Florence. Though our expectations are but slender, we do not entirely despair of seeing this curious relic dug out of some Italian library or other.

Appended to the Life of Dr. Edward Bernard, published in Latin by Dr. Thomas Smith, London 1704, is a collection, entitled "Veterum Mathematicorum scripta quæ reperiri potuerunt, voluminibus XIV." This is either a collection of works which Bernard had made, or a synopsis of such a collection as he conceived might have

* The following passages are from the letters of M. to the writer: "Le manuscrit original de Harmonicon Cœleste est à Florence. Bouilland, astronome Français, a prêté ce livre, en 1662, au prince Leopold de Toscane, protecteur de l'académie del Cimento." On some surprise being expressed at this, in connexion with Bouillaud's printed assertion in early life, the following confirmation was given: "Le fait concernant le manuscrit de Harmonicon Caeleste, prêté par Bouillaud au prince Leopold des Medicis est consigné dans les manuscrits de Bouillaud, et M. (naming a very celebracted mathematician) "savant géométre, m'en a donné l'assurance. Il faut chercher dans les manuscrits, ou dans les ouvrages publiés par les auteurs, la verité de l'histoire."

been made. But he says, page 23, "accedant quædam de Vieta Harmonico Coelesti; cujus mentio in Astronomia Philol." Whether this be actual or hypothetical, might be ascertained by examination of Bernard's manuscripts, if he left any: Bernard was Savilian professor at Oxford, and died in 1703, being succeeded by Dr. Gregory. IV.-Chaucer's work on the Astrolabe. This astronomical work of our oldest poet is the first work on any science in English of which we have any knowledge. It was written (says the black-letter edition of Chaucer, of 1602) in 1391, and the preface will show to whom and why.

"Little Lowis my sonne, I perceiue well by certaine euidences, thine abilitie to learne sciences touching numbers and proportions, and also wel consider I thy busie prayer in especiall to learne the Treatise of the Astrolabie. Then for as much as a philosopher saith, he wrapeth him in his friend, that condiscendeth to the rightfull prayers of his friend. Therefor I haue giuen thee a sufficient Astrolabie for our orizont, compouned after the latitude of Oxenford: upon the which, by meditation of this little treatise, I purpose to teach thee a certaine number of conclusions pertayning to this same instrument. I say a certaine [number] of conclusions, for three causes, the first cause is this: Trust well, that all the conclusions that haue be founden, or els possibly might bee found in so noble an instrument as in the Astrolaby, ben unknowen perfitly to any mortall man in this region, as I suppose. Another cause is this, that soothly in any carts of the Astrolabie that I haue yseene, there ben some conclusions, that woll not in all thyngs perfourme her behests; and some of hem beene too hard to thy tender age of ten yeare, to conceiue. This treatise deuided in fiue parts, will I shewe the woonder-light rules and naked words in English, for Latine ne canst thou not yet but smale, my little sonne. But neuer the lesse, suffiseth to thee these true conclusions in English, as well as sufficeth to this noble clerkes, Greekes, these same conclusions in Greeke, and to the Arabines in Arabike, and to Jewes in Hebrewe, and to the Latin folke in Latine; which Latin folke had

hem first out of other diuers languages, and writ hem in her owne tongue, that is to saine, in Latine.

"And God wote that in all these languages, and in many mo, haue these conclusions been sufficiently learned and taught, and yet by diuers rules, Right as diueres pathes leaden diuers folke the right way to Rome.

"Now woll I pray meekely euery person discreet, that redeth or heareth this little treatise, to haue my rude ententing excused, and my superfluitie of words, for two causes: The first cause is, for that curious enditing, and hard sentences, is full heauy at once for such a child to learne: And the second cause is this, that sothly me semeth better to writen unto a child twice a good sentence, than he foryete it once. And Lowis, if it so be that I shew thee in my lith English, as true conclusions touching this matter, and not only as true, but as many and subtill conclusions, as ben yshewed in Latine, in any common treatise of the Astrolabie, conne me the more thanke, and pray God saue the king, that is lord of this langage, and all that him faith beareth and obeyeth, eueriche in his degree, the more and the lesse. But considereth well, that I ne usurp not to haue founden this work of my labouror of mine engine: I nam but a leaud compilatour of the labour of olde Astrologiens, and haue it translated in mine English, only for thy doctrine and with this swerde shall I sleen enuie."

and

Chaucer does not seem to have finished this work, for in the beginning he divided it into six parts, of which only the first and second, (at most,) have been either finished by him, or else preserved to us. He says that the third part "shall contayne diuers tables of longitudes and latitudes of sterres, fixe in the Astrolabie ; tables of the declinations of the sun, and tables of the longitude of citties and townes: and tables as well for the gouernation of the clocke, as for to finde the altitude meridian," &c. Nothing of this appears in the work, which consists of a description of the instrument called the astrolabe, and directions how to use it.

Mr. Peacock, in that excellent and enormous pile of researches which is called by the simple name of " Arith