We have noticed that the notation A:B::C:D antedates the year 1657. Vincent Wing, the astronomer, published in 1651 in London the Harmonicon coeleste, in which is found not only Oughtred’s notation A.B::C.D but also the modified form of it given above. The two are used interchangeably. His later works, the Logistica astronomica (1656), Doctrina spherica (1655), and Doctrina theorica, published in one volume in London, all use the symbols A:B::C:D exclusively. The author of a book entitled, An Idea of Arithmetick at first designed for the use of the Free Schoole at Thurlow in Suffolk . . . . by R. B., Schoolmaster there, London, 1655, writes A:a::C:c, though part of the time he uses Oughtred’s unmodified notation. We can best indicate the trend in England by indicating the authors of the seventeenth century whom we have found using the notation A:B::C:D and the authors of the eighteenth century whom we have found using A.B::C.D. The former notation was the less common during the seventeenth but the more common during the eighteenth century. We have observed the symbols A:B::C:D (besides the authors already named) in John Collins (1659),[93] James Gregory (1663),[94] Christopher Wren (1668-69),[95] William Leybourn (1673),[96] William Sanders (1686),[97] John Hawkins (1684),[98] Joseph Raphson (1697),[99] E. Wells (1698),[100] and John Ward (1698).[101] Of English eighteenth-century authors the following still clung to the notation A.B::C.D: John Harris’ translation of F. Ignatius Gaston Pardies (1701),[102] George Shelley (1704),[103] Sam Cobb (1709),[104] J. Collins in Commercium Epistolicum (1712), John Craig (1718),[105] Jo. Wilson (1724).[106] The latest use of A.B::C.D which has come to our notice is in the translation of the Analytical Institutions of Maria G. Agnesi, made by John Colson sometime before 1760, but which was not published until 1801. During the seventeenth century the notation A:B::C:D acquired almost complete ascendancy in England. In France Oughtred’s unmodified notation A.B::C.D, having been adopted later, was also discarded later than in England. An approximate idea of the situation appears from the following data. The notation A.B::C.D was used by M. Carré (1700),[107] M. Guisnée (1705),[108] M. de Fontenelle (1727),[109] M. Varignon (1725),[110] M. Robillard (1753),[111] M. Sebastien le Clerc (1764),[112] Clairaut (1731),[113] M. L’Hospital (1781).[114] In Italy Oughtred’s modified notation a, b::c, d was used by Maria G. Agnesi in her Instituzioni analitiche, Milano, 1748. The notation a:b::c:d found entrance the latter part of the eighteenth century. In Germany the symbolism a:b=c:d, suggested by Leibniz, found wider acceptance.[115]