Eighth preliminary edition

This book has traditionally been attributed (since 1643) to Père Jean Leurechon, SJ (c1591-1670), who was probably van Etten's university teacher, but the book specifically names van Etten and there seems to be very little real evidence for Leurechon's authorship. Trevor Hall's booklet and chapter are a substantial study of this question and he concludes that there is no real reason to doubt van Etten's authorship, though he may well have had help or inspiration from his teacher. Hall has also shown that van Etten and his uncle, the book's dedicatee, were real people. (Toole Stott 429 431 dismisses Hall's work as a result of completely misunderstanding it!) However, the book was amended, revised and translated many times, so that versions may occur under the following names: Hendrik van Etten; Jean Leurechon; D.H.P.E.M. = Denis (or Didier) Henrion, professeur en mathématique (or Professeur ès Mathematiques), a pseudonym of Clément Cyriaque de Mangin, who also called himself Pierre Hérigone; Claude Mydorge; Caspar (or Gaspar) Ens; Wynant van Westen; William Oughtred; William Leake; not to mention Anonymous and versions of the title -- I have found it under Recreations or Récréations and under Vermakelijkheden. E.g. Lucas, RM1, 239-240, has 7 entries for this book under five different authors and twice under Récréations.

Jacques Voignier; Who was the author of "Recreation Mathematique" (1624)?; The Perennial Mystics #9 (1991) 5-48 (& 1-2 which are the cover and its reverse). [This journal is edited and published by James Hagy, 2373 Arbeleda Lane, Northbrook, Illinois, 60062, USA.] This is the second serious study of this book. He points out evidence for Leurechon's connection with the book, which makes it seem more likely, but definite evidence is still lacking, so I am suggesting that it may have been some kind of joint production and I will change my references it to van Etten/Leurechon. The work of Hall and Voignier form the basis of the following discussion, supplemented by the standard catalogues and personal inspection of about a half of the French and English editions -- generally after 1630.
Henrik van Etten. Recreation Mathematicque. Composee de Plusieurs Problemes Plaisants et Facetieux. En faict d'Arithmeticque Geometrie, Mechanicque, Opticque, & autres parties de ces belles sciences. Jean Appier Hanzelet, Pont a Mousson, 1624 [taken from facsimile of the 1626 ed.]. 155pp., ??NYS.

2nd ed., 1626, ibid. = recent facsimile with no details, but with 'Pont à Mousson 13   10   54' written inside the back cover. [An apparently identical copy at the Museum of the History of Science, Oxford, has a small insert saying it was reissued by La Compagnie de Pont-à-Mousson, printed by l'Imprimerie Berger-Levrault, nd.]. 91 problems on xiv + 144 = 158pp. [The extra pages include questions V and VI of problem 91 -- these questions occur in no other edition, except probably in the 1629 reissue in Pont-à-Mousson.]

After the two Hanzelet editions, there were three editions in Paris in 1626, by Rolet Boutonné (2nd ed.), by Antoine Robinot (2nd ed.) and by Jean Moreau & Guillaume Loyson (3rd ed.). Boutonné and Robinot were closely associated and their output was interchangeable. Their 2nd eds. appear to be essentially the 1624 ed. The Moreau & Loyson has Notes added to the problems and 8pp. of Additions. This was the first to put the illustrations as woodcuts in the text rather than using copperplates for five separate sheets of 8 figures. The Notes are signed D.A.L.G., but are due to Claude Mydorge. (NUC indicates the Robinot had further comments signed D.H.P.E.M., later identified as Denis (or Didier) Henrion Professeur En Mathématique (though Henrion is a pseudonym of Clément Cyriaque de Mangin!) -- but this seems to be a confusion.) In the next few years, editions appeared in Paris, Rouen and Lyon. In 1627, Boutonné issued a '4th ed.' with "Nottes sur les recreations mathematiques ... Par D. H. P. E. M." and the D.A.L.G. notes were omitted. In 1627, Claude Rigaud & Claude Obert, Lyon, issued a version with 9pp of Additions as in the 1626 Moreau & Loyson.

In 1628, Charles Osmont, Rouen, issued a version in three parts: Récréations mathématiques ... 1^re et 2^de partie. La 3^e partie contient un recueil de plusieurs gentilles et récréatives inventions de feux d'artifice .... Part 1 was van Etten's 91 problems, with questions V & VI of prob. 91 omitted, omitting the D.A.L.G. notes and the Additions. Part 2 had 45 new problems, often attributed to Mydorge and/or Henrion, but they had no connection with this and the authorship of these problems is unknown, though Voignier suggests the printer, Osmont. Part 3 is an independent treatise on fireworks which Hall attributes to Hanzelet. This edition was reissued in Rouen by various publishers in 1628, 1629, 1630, 1634, 1638 and in Lyon in 1642-1643, 1653, 1656, 1658, 1669, 1680.

In 1630, Boutonné and Robinot (their printing is indistinguishable and volumes often have parts from both of them, indeed the Privilege is issued to them jointly) issued an extended version in four parts, titled Examen du Livre des Recreations Mathematiques, stated to be by Mydorge. Part 1 is van Etten's 91 problems, with parts V & VI of prob. 91 omitted, with many problems being followed by an Examen signed D.A.L.G. These are by Mydorge and are a revision of his material in the 1626 Moreau & Loyson. Part 2 has its own TP and had 45 new problems, taken from the 1628 Rouen ed. Part 3 has its own TP, but doesn't state the publisher, and is the independent treatise on fireworks, also taken from the 1628 Rouen ed. Part 4 again has its own TP and is Nottes [sic] sur les Recreation Mathematiques by D.H.P.E.M. and are additions to 27 of van Etten's problems, taken or extended from the Notes in the 1627 4th ed. The book is also described as 3 parts with the Nottes, but Parts 2 and 3 are consecutively paged, leading to some descriptions of the book as being in 3 parts. The parts were probably issued separately as they sometimes are catalogued separately and different copies of the whole work often have a mixture of the Boutonné and Robinot printings. This most extended form was reissued by various publishers in Paris: 1634(??), 1638, 1639, and in Rouen: 1639 (two publishers), 1643 (two publishers ??), 1648?, 1649?

In 1659, Cardin Besonge, Paris, issued Les Récréations mathématiques, avec l'examen de ses problèmes en arithmétique, géométrie, .... Premièrement reveu par D. Henrion, depuis par M. Mydorge, et tout nouvellement corrigé et augmenté, 5^e et dernière édition. The Nottes are incorporated in the text (or perhaps omitted??). The entire text is consecutively page-numbered. Reissued in Paris: 1660, 1661 and in Rouen as the 6th ed.: 1660?, 1663?, 1664, 1669 (seven publishers!).

The 1630 Paris ed. and the 1626 ed. have the same problem numbers for the first 91 problems, as do almost all French editions. I will cite the problem number and the pages of the 1626 ed. I will add reference to the 1630 Paris ed., when the latter has additional information. Only one of the additional problems in part 2 (prob. 7) is of any interest to us, but several of Henrion's Nottes give corrections, extensions, additional references and even additional problems. I didn't find any of the D.A.L.G. notes of any interest.
English editions.

Mathematicall Recreations. Or a Collection of sundrie [1653 has: many] Problemes, extracted out of the Ancient and Moderne Philosophers, as secrets in nature, and experiments in Arithmeticke, Geometrie, Cosmographie, Horologographie, Astronomie, Navigation, Musicke, Opticks, Architecture, Staticke, Machanicks, Chimestrie, Waterworkes, Fireworks, &c. Not vulgarly made manifest untill this time: Fit for Schollers, Students, and Gentlemen, that desire to know the Philosophicall cause of many admirable Conclusions. Usefull for others, to acuate and stirre them up to the search of further knowledge; and serviceable to all for many excellent things, both for pleasure and Recreation. Most of which were written first in Greeke and Latine, lately compiled in French, by Henry Van Etten Gent. And now delivered in the English tongue, with the Examinations, Corrections, and Augmentations. Printed by T. Cotes for Richard Hawkins, London, 1633. 328pp. (This ed. is 'excessively rare'.)

Reissued by William Leake, London: 2nd ed., 1653; (1667(??)); 1674. 344pp. [Hall, OCB, says the 2nd ed. is similar to the 1633 edition, but with an extra 16pp description (of 1636) of some dials by Oughtred (which led to the book or the translation often being attributed to Oughtred). Hall also states that the English editions are based on the Rouen ed. of 1628. Sadly some interesting problems were omitted in the English, leading to confusion in plate numbers. However, I have just noticed that Prob. 63 is about two pages longer than the corresponding Prob. 70 of the French editions.] The 1633, 1653 and 1674 editions are identical except for the additional English material in the later editions. I will add citations to the English editions in parentheses. I now have an imperfect copy of the 1674 ed, covers missing and lacking the Frontispiece and pp. 273-282 and later material. Heyl 311 is a 1753 ed., which must be an error for 1653.

W. Leybourn, qv, takes several sections directly from the English editions.

Latin editions.

In 1628(??), Caspar (or Gaspar) Ens made a Latin translation but added some other material, e.g. 49 problems from Alcuin. I have only studied the 1636 ed. carefully.

Thaumaturgus Mathematicus, Id est, Admirabilium Effectorum e Mathematicarum Disciplinarum Fontibus Profluentium Sylloge. Casparo Ens L. Collectore & Interprete. 1628. [Taken from 1636 TP. MUS #30 says this is only a translation of van Etten. There is some doubt whether the 1628 edition exists!]

Reissued in 1636 and 1651. It has 89 of van Etten's problems (omitting 38 & 46) and adding 25 new problems, with some numbering errors so the last is numbered 113. This is followed by 55 problems of Alcuin, using the Bede version of 56 problems, but omitting 18.

Thaumaturgus mathematicus Gasparo Ens lectore collectore, & interprete, Nunc denuò Correctus, & Auctus. Apollonius Zambonus, Venice, 1706. 113 problems + 49 from Alcuin (check??). There are some differences between this and the 1636 ed.

[MUS #30 gives Köln, 1651, and further editions.]

Dutch editions.

In 1641, Wynant van Westen translated van Etten into Dutch. The title is: Het eerste [- derde] deel van de Mathematische vermaecklyckheden. Te samen ghevoeght van verscheyden ghenuchlijcke ende boertige werckstucken, soo uyt arithmetica, geometria, astronomie, geographia, cosmographia, musica, physica, optica, catoptrica, architectonica, sciotetica, als uyt andere ongehoorde mysterien meer. Ghetranslateert uyt het fransch in nederduytsche tale: ende verrijckt, vermeerdert, ende verbetert met verscheyden observatien ende annotatien, dienende tot onderrichtinge van eenige duystere questien, ende mis-slaghen in den franschen druck. Door Wynant van Westen .... op nieus oversien verbetert. Jacob van Biesen, Arnhem, 1641. 3 parts with separate title pages and pagination, perhaps in 3 vols, but later in 1 vol.

This was reissued: Van Biesen, Arnhem, 1641, ??, 1644, 1662, 1671-72; Lootsman and Jacobsz, Amsterdam, 1673. I haven't examined any of these.
Euler. Algebra. 1770.

Leonard Euler (1707-1783). Vollständig Anleitung zur Algebra. Royal Academy of Sciences at Petersburg, 1770. [A Russian translation appeared in 1768.] Translated into French by John III Bernoulli, with additions by Bernoulli and La Grange (pp. 463-593 here), 1774. Translated from French into English as Element of Algebra, with further notes, by Rev. John Hewlett, with a Memoir of Euler by Francis Horner [Horner actually did the translation; Hewlett edited it.], (1797), 5th ed., Longman, Orme, and Co., London, 1840. Reprinted, with Introduction by C. Truesdell (1972), omitting 4 pp of Horner, Springer, NY, 1984 [hidden on back of title page]. I will cite part, section, chapter, article and the pages from the Springer ed. (Part II has no sections.) Unfortunately these numbers seem to have little connection with other editions. [Though most of the recreational material in Euler is much older than Euler, I have included it as a representative 18C text.] [Halwas 175-176 are some US editions -- the 1818 edition was the first example of a translated algebra in the US.]

Family Friend. The Family Friend. This was a magazine founded by Robert Kemp Philp in 1849. The dating is awkward -- vol. 1 is dated 1850 on the cover, but the Preface is dated 15 Nov 1849 and refers to the success of the past year, when it appeared monthly. It also says the magazine will henceforth appear twice a month with two volumes per year, due on the first of June and December. The Gardening section of vol. 1 goes from Jan to Dec. The Preface of Vol. 2 is dated 10 Jun 1850 and its gardening section covers Jan - Jun. The Preface of Vol. 3 is dated 15 Dec 1850 and its Gardening section goes Jul - Dec. BMC shows Philp left in 1852 and the magazine continued with two volumes per year through a fifth series, ending in 1867, then restarted with one volume a year from 1870 until 1921. I have vols. 1 - 3 & the second half of 1858, which is dated 1858-9, but appears to be Jul-Dec. None of the text is signed. At the back of volumes are included answers to correspondents. The puzzles are often identical to those in The Magician's Own Book or The Illustrated Boy's Own Treasury, etc., but are considerably earlier.

FHM. Graham Flegg, Cynthia Hay & Barbara Moss -- see under Chuquet.

Fibonacci. Leonardo Pisano, called Fibonacci (c1170->1240). Liber Abbaci. (1202); 2nd ed., 1228. In: Scritti di Leonardo Pisano; vol. I, ed. and pub. by B. Boncompagni; Tipografia delle Scienze Matematiche e Fisiche, Rome, 1857. The title pages give 'abbaci', but Boncompagni's text begins 'Incipit liber Abaci ... Anno MCCII.', while the c1275 MS starts 'Incipit abbacus'. Both forms are used, sometimes even in the same article -- e.g. Loria's biographical article, see in Section 1.

Richard E. Grimm was working on a critical edition of this and he kindly gave me some details. There are 15 known MSS, all of the 1228 2nd ed. Six of these consist of 1½ to 3 chapters only; five of the others lack Chapter 10 and the second half of Chapter 9; one lacks Chapter 10 and one lacks much of Chapter 15, leaving two essentially complete texts. The last four MSS mentioned are the most important: Siena L.IV.20, c1275, lacking much of Chap. 15, "the oldest and best"; Siena L.IV.21, 1463 [Grimm said c1465 -- there are dates up through 1464 in interest calculations, but the Incipit specifically says 1463], which includes much other material from later writers, so it is at least double the size of L.IV.20; Vatican Palatino #1343, end of 13C, lacking Chap. 10; Florence Bibl. Naz. Conventi Soppressi C. 1. 2616, early 14C, "handsome but frequently badly faded" so "that a later hand found it necessary to rewrite what he saw there." When I examined it in Sep 1994, the black ink was indeed sometimes badly faded but the numbers were in a clear red -- perhaps these are what was rewritten?? L.IV.20 has the beginning sentence ending "et correctus ab eodem a MCCXXVIII", but Grimm says all the others are also of the 1228 ed even if they do not carry this addition or the extra initial dedication. Sadly, I heard in Aug 1998 that Grimm had Alzheimer's disease and was in a nursing home. Inquiry has revealed no trace of the photocopies of all the Liber Abbaci MSS which he said he had obtained and in summer 2000 I heard he had died.

Boncompagni used only one MS, then denoted Codex Magliabechiana, C. I, 2616, Badia Fiorentina, no. 73, now Conventi Soppressi, C. I. 2616, the badly faded fourth MS described above.

In Sep 1994 and Mar 1998, I examined Siena L.IV.20 and 21 and Conv. Soppr. C.1.2616. I have slides of the Incipit & Fibonacci numbers from all of these and some other material.

The dates of 1202 and 1228 are based on the Pisan calendar.

Fibonacci-Sigler. Liber Abaci. Translated by Laurence E. Sigler as: Fibonacci's Liber Abaci A Translation into Modern English of Leonardo Pisano's Book of Calculation. Springer, New York, 2002. I have added page references to this, denoted S, after the Boncompagni pages, e.g. pp. 397-398 (S: 543-544). I have given Sigler's English wherever I previously had just quoted the Latin.

Fibonacci. Flos and Epistola.

Leonardo Pisano, called Fibonacci. MS of c1225 which begins "Incipit flos Leonardi bigolli pisani ...", Biblioteca Ambrosiana, Milan, E. 75. In: Scritti di Leonardo Pisano, vol. II, ed. and pub. by B. Boncompagni, Rome, 1862, pp. 227-252.

Part of the MS has a separate heading: "Epistola suprascripsit Leonardi ad Magistrum Theodorum phylosophum domini Imperatoris" and is sometimes considered a separate work. It occupies pp. 247-252 of the printed version. For an English description, see: A. F. Horadam; Fibonacci's mathematical letter to Master Theodorus; Fibonacci Quarterly 29 (1991) 103-107.

Italian translation (including the Epistola) and commentary: E. Picutti; Il 'Flos' di Leonardo Pisano; Physis 25 (1983) 293-387.

Fireside Amusements. 1850.

Fireside Amusements. Chambers's Library for Young People. William and Robert Chambers, Edinburgh, 1850, 188pp. The BMC has this under Fireside Amusements and refers to Chambers for the Library, which was 19 vols, 1848-1851. Pp. 187+ are missing in the copy I have seen, but it seems that just one page of solutions is missing -- the NUC gives 188pp. The NUC lists a 1870 reprint.

[The BMC lists an 1880 ed with 159pp, part of Chambers's Juvenile Library, NYS.]

Fireside Amusements A Book of Indoor Games. W. & R. Chambers, London and Edinburgh, nd, 128pp. The BMC lists this as 1890[1889]. Though laid out entirely differently, almost all the material is taken from the 1850 ed. I will cite both editions.

Much of the material of interest is taken from Child: Girl's Own Book.

Folkerts. Aufgabensammlungen. 13-15C.

Menso Folkerts. Mathematische Aufgabensammlungen aus dem ausgehenden Mittelalter. Sudhoffs Archiv 55 (1971) 58-75. He examines 33 anonymous Latin manuscript problem collections from 13-15 C in Oxford, London, Berlin, Munich, Vienna and Erfurt and catalogues the problems therein. Of these, only Munich 14684 is published (cf below). He notes that many more such sources exist. His catalogue covers 14 of my topics. I will not try to cite the individual MSS, since many of the topics occur in over a dozen of them. I will simply say he has n sources, though some of the sources have several examples.

Folkerts, Menso. See: Alcuin.

della Francesca. Trattato. c1480.

Piero della Francesca (1412-1492). Trattato d'Abaco. Italian MS in Codex Ashburnhamiano 359* [291*] - 280 in the Biblioteca Mediceo-Laurenziana, Florence. c1480 [according to Van Egmond's Catalog 84, based on watermarks in the paper which date from 1470 to 1500, but Davis, below, p. 16, says c1450]. Transcribed and annotated by Gino Arrighi, Testimonianze di Storia della Scienze 6, Domus Galilæana, Pisa, 1970. Arrighi uses c. (for carta) instead of f. (for folio), but I will use f. for consistency with other usage, followed by the pages in Arrighi in ( ). Arrighi reproduces many of the diagrams, but he doesn't say anything about whether he has included all of them. This MS appears to be that which was in the possession of Piero's descendents until 1835 when it was reported as having disappeared. Guglielmo Libri, the noted historian of mathematics, who was also a shady bookdealer, transcribed part of this MS in vol. 3 of his Histoire de la Mathématique en Italie in 1840 as an anonymous work, then sold it to Lord Ashburnham in 1847 (recorded in his collection in 1881) whose collection was bought for the Laurentian Library in 1884. There are three different catalogue numbers - I use the format used in Van Egmond's Catalog. The MS had passed out of common knowledge until it was rediscovered in the Laurentian Library in 1917 by Girolamo Mancini who recognised the handwriting as Piero's.

This work and Piero's Libellus de Quinque Corporibus Regularibus are the subject of a long standing plagiarism argument. Giorgio Vasari [Le Vite de' più eccellenti pittori, scultori e architetti; 1550; The Essential Vasari, ed. by Betty Burroughs from the 1850 translation of Mrs. Jonathan Foster, Unwin Books, London, 1962] states: "... Piero della Francesca, who was a master of perspective and mathematics but who first went blind and then died before his books were known to the public. Fra Luca di Borgo, who should have cherished the memory of his master and teacher, Piero, did his best, on the contrary, to obliterate his name, taking to himself all the honour by publishing as his own work that of that good old man. ... Maestro Luca di Borgo caused the works of his master, Piero della Francesca, to be printed as his own after Piero died." The mathematical works of Piero were unknown until they were rediscovered in 1850/1880 and 1917. Examination shows that Pacioli certainly used 105 problems, many unusual, from Piero in the Summa. But he does praise Piero in the Epistola (f. 2r) of the Summa, as "the monarch of painting of our times". It has been suggested that Pacioli had a large hand in the writing of Piero's works and hence was just reusing his own material and he frequently expands on it. However, there is no evidence that Pacioli was ever a student of Piero. Entire books have been written on the question, so I will not try to say any more. See: Margaret Daly Davis; Piero della Francesca's Mathematical Treatises The "Trattato d'abaco" and "Libellus de quinque corporibus regularibus"; Longo Editore, Ravenna, 1977, for detailed comparisons and the work of R. E. Taylor in Section 1: Pacioli. Davis identifies 139 problems in the Libellus, of which 85 (= 61%) are taken from the Trattato. Davis notes that Pacioli's Summa, Part II, ff. 68v   73v, prob. 1-56, are essentially identical to della Francesca's Trattato, ff. 105r   120r. See also section 6.AT.3 where the Libellus and the Pacioli & da Vinci: De Divina Proportione are discussed.

The work is discussed and 42 problems are given in English in: S. A. Jayawardene; The 'Trattato d'Abaco' of Piero della Francesca; IN: Cecil H. Clough, ed.; Cultural Aspects of the Italian Renaissance Essays in Honour of Paul Oskar Kristeller; Manchester Univ. Press, Manchester, nd [1976?]; pp. 229-243. I will note 'English in Jayawardene.' when relevant.

Frikell, Wiljalba (1818 (or 1816) - 1903). (The given name Gustave sometimes occurs -- I thought Gustave might be a son of Wiljalba, but the son was named Adalbert ( -1889) and his name was pirated by a clumsy imposter in England.)

See the discussion at: Book of 500 Puzzles, Boy's Own Conjuring Book, Hanky Panky, Magician's Own Book, The Secret Out. Frikell was a noted conjuror of the time and his name has been associated with the UK versions of these books, but there is no evidence he had anything to do with them. The Art of Amusing, by Frank Bellew, Hotten, London, 1866?, op. cit. in 5.E, has a note on the back of the TP saying The Secret Out is a companion volume, just issued, by Hermann Frikell. C&B, under Williams, Henry Llewellyn ("W. Frikell") lists: Hanky Panky; Magician's Own Book, London & New York; (Magic No Mystery); The Secret Out and says to also see Cremer.

Gamow & Stern. 1958.

George Gamow & Marvin Stern. Puzzle Math. Macmillan, London, 1958.

Gardner. Martin Gardner (1914- ). Many references are to both his SA column, cited by (month & year), e.g. SA (Mar 1982), and to the appearance of the column as a chapter in one of his books, abbreviated as shown below. In general, I will only give the chapter reference as the various editions and translations are differently paginated. Answers, comments and extensions appeared in succeeding issues of SA, usually in Gardner's column, but sometimes in the Letters. All this material is collected in the book chapter, sometimes by rewriting of the article, sometimes as notes or an Addendum at the end of the chapter. Since many years usually passed before the book version, the Addenda often contain material that never appeared in SA, as well as references to work done as a result of the SA article. I have not tried to enter all of Gardner's references here, so anyone interested in a topic that Gardner has considered should consult the book version of Gardner's column. Currently some of the earlier books are being reissued in new editions, with further extensions and updating. See also the next entry.

For years from at least 1950, SA appeared in two volumes per year, each of six issues. In year 1950 + n, vol. 182 + 2n covers Jan-Jun and vol. 183 + 2n covers Jul-Dec.