Oughtred does not express aggregation by (). Parentheses had been used by Girard, and by Clavius as early as 1609,[28] but did not come into general use in mathematical language until the time of Leibniz and the Bernoullis. Oughtred indicates aggregation by writing a colon (:) at both ends. Thus, Q:A-E: means with him (A-E)². Similarly, √q:A+E: means √(A+E). The two dots at the end are frequently omitted when the part affected includes all the terms of the polynomial to the end. Thus, C:A+B-E=.. means (A+B-E)³=.. There are still further departures from this notation, but they occur so seldom that we incline to the interpretation that they are simply printer’s errors. For proportion Oughtred uses the symbol (::). The proportion a:b=c:d appears in his notation a·b::c·d. Apparently, a proportion was not fully recognized in this day as being the expression of an equality of ratios. That probably explains why he did not use = here as in the notation of ordinary equations. Yet Oughtred must have been very close to the interpretation of a proportion as an equality; for he says in his Elementi decimi Euclidis declaratio, “proportio, sive ratio aequalis ::” That he introduced this extra symbol when the one for equality was sufficient is a misfortune. Simplicity demands that no unnecessary symbols be introduced. However, Oughtred’s symbolism is certainly superior to those which preceded. Consider the notation of Clavius.[29] He wrote 20:60=4:x, x=12, thus: “20·60·4? fiunt 12.” The insufficiency of such a notation in the more involved expressions frequently arising in algebra is readily seen. Hence Oughtred’s notation (::) was early adopted by English mathematicians. It was used by John Wallis at Oxford, by Samuel Foster at Gresham College, by James Gregory of Edinburgh, by the translators into English of Rahn’s algebra, and by many other early writers. Oughtred has been credited generally with the introduction of St. Andrew’s cross × as the symbol for multiplication in the Clavis of 1631. We have discovered that this symbol, or rather the letter x which closely resembles it, occurs as the sign of multiplication thirteen years earlier in an anonymous “Appendix to the Logarithmes, shewing the practise of the Calculation of Triangles etc.” to Edward Wright’s translation of John Napier’s Descriptio, published in 1618.[30] Later we shall give our reasons for believing that Oughtred is the author of that “Appendix.” The × has survived as a symbol of multiplication. Another symbol introduced by Oughtred and found in modern books is ~, expressing difference; thus C~D signifies the difference between C and D, even when D is the larger number.[31] This symbol was used by John Wallis in 1657.[32] Oughtred represented in symbols also certain composite expressions, as for instance A+E=Z, A-E=X, where A is greater than E. He represented by a symbol also each of the following: A²+E², A³+E³, A²-E², A³-E³.