In all there appeared five Latin editions, the second in 1648 at London, the third in 1652 at Oxford, the fourth in 1667 at Oxford, the fifth in 1693 and 1698 at Oxford. There were two independent English editions: the first in 1647 at London, translated in greater part by Robert Wood of Lincoln College, Oxford, as is stated in the preface to the 1652 Latin edition; the second in 1694 and 1702 is a new translation, the preface being written and the book recommended by the astronomer Edmund Halley. The 1694 and 1702 impressions labored under the defect of many sense-disturbing errors due to careless reading of the proofs. All the editions of the Clavis, after the first edition, had one or more of the following tracts added on: Eq.=De Aequationum affectarvm resolvtione in numeris. Eu.=Elementi decimi Euclidis declaratio. So.=De Solidis regularibus, tractatus. An.=De Anatocismo, sive usura composita. Fa.=Regula falsae positionis. Ar.=Theorematum in libris Archimedis de Sphaera & cylindro declaratio. Ho.=Horologia scioterica in plano, geometricè delineandi modus. The abbreviated titles given here are, of course, our own. The lists of tracts added to the Clavis mathematicae of 1631 in its later editions, given in the order in which the tracts appear in each edition, are as follows: Clavis of 1647, Eq., An., Fa., Ho.; Clavis of 1648, Eq., An., Fa., Eu., So.; Clavis of 1652, Eq., Eu., So., An., Fa., Ar., Ho.; Clavis of 1667, Eq., Eu., So., An., Fa., Ar., Ho.; Clavis of 1693 and 1698, Eq., Eu., So., An., Fa., Ar., Ho.; Clavis of 1694 and 1702, Eq. The title-page of the Clavis was considerably modified after the first edition. Thus, the 1652 Latin edition has this title-page: Guilelmi Oughtred Aetonensis, quondam Collegii Regalis in Cantabrigia Socii, Clavis mathematicae denvo limata, sive potius fabricata. Cum aliis quibusdam ejusdem commentationibus, quae in sequenti pagina recensentur. Editio tertia auctior & emendatior. Oxoniae, Excudebat Leon. Lichfield, Veneunt apud Tho. Robinson. 1652. [23]Rigaud, op. cit., Vol. II, p. 476. [24]See, for instance, the Clavis mathematicae of 1652, where he expresses himself thus (p. 4): “Speciosa haec Arithmetica arti Analyticae (per quam ex sumptione quaesiti, tanquam noti, investigatur quaesitum) multo accommodatior est, quam illa numerosa.” [25]Oughtred, The Key of the Mathematicks, London, 1647, p. 4. [26]Clavis 1694, p. 19, and the Clavis of 1631, p. 8. [27]See for instance, Oughtred’s Elementi decimi Euclidis declaratio, 1652, p. 1, where he uses A and E, and also a and e. [28]See Christophori Clavii Bambergensis Operum mathematicorum, tomus secundus, Moguntiae, M.DC.XI, algebra, p. 39. [29]Christophori Clavii operum mathematicorum Tomus Secundus, Moguntiae, M.DC.XI, Epitome arithmeticae, p. 36.