The symbol for the arithmetical difference between two numbers, ~, is usually attributed to John Wallis, but it occurs in Oughtred’s Clavis mathematicae of 1652, in the tract on Elementi decimi Euclidis declaratio, at an earlier date than in any of Wallis’ books. As Wallis assisted in putting this edition through the press it is possible, though not probable, that the symbol was inserted by him. Were the symbol Wallis’, Oughtred would doubtless have referred to its origin in the preface. During the eighteenth century the symbol found its way into foreign texts even in far-off Italy.[122] It is one of three symbols presumably invented by Oughtred and which are still used at the present time. The others are × and ::. The curious and ill-chosen symbols, |̲̅ ̅ for “greater than,” and ̲ ̲̅| for “less than,” were certain to succumb in their struggle for existence against Harriot’s admirably chosen > and <. Yet such was the reputation of Oughtred that his symbols were used in England quite extensively during the seventeenth and the beginning of the eighteenth century. Considerable confusion has existed among algebraists and also among historians as to what Oughtred’s symbols really were. Particularly is this true of the sign for “less than” which is frequently written ̅ ̲̅|. Oughtred’s symbols, or these symbols turned about in some way, have been used by Seth Ward,[123] John Wallis,[124] Isaac Barrow,[125] John Kersey,[126] E. Wells,[127] John Hawkins,[128] Tho. Baker,[129] Richard Sault,[130] Richard Rawlinson,[131] Franciscus Dulaurens,[132] James Milnes,[133] George Cheyne,[134] John Craig,[135] Jo. Wilson,[136] and J. Collins.[137] General acceptance has been accorded to Oughtred’s symbol ×. The first printed appearance of this symbol for multiplication in 1618 in the form of the letter x hardly explains its real origin. The author of the “Appendix” (be he Oughtred or someone else) may not have used the letter x at all, but may have written the cross ×, called the St. Andrew’s cross, while the printer, in the absence of any type accurately representing that cross, may have substituted the letter x in its place. The hypothesis that the symbol × of multiplication owes its origin to the old habit of using directed bars to indicate that two numbers are to be combined, as for instance in the multiplication of 23 and 34, thus, 2 3 |\ /| | x | |/ \| 3 4 ------- 7 8 2 has been advanced by two writers, C. Le Paige[138] and Gravelaar.[139] Bosmans is more inclined to the belief that Oughtred adopted the symbol somewhat arbitrarily, much as he did the numerous symbols in his Elementi decimi Euclidis declaratio.[140] Le Paige’s and Gravelaar’s theory finds some support in the fact that the cross ×, without the two additional vertical lines shown above, occurs in a commentary published by Oswald Schreshensuchs[141] in 1551, where the sign is written between two factors placed one above the other.