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Leibniz's notation
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==Other notations of Leibniz== Leibniz experimented with many different notations in various areas of mathematics. He felt that good notation was fundamental in the pursuit of mathematics. In a letter to l'Hôpital in 1693 he says:<ref name="Cajori185">{{harvnb|Cajori|1993|loc=Vol. II, p. 185}}</ref> {{quote|One of the secrets of analysis consists in the characteristic, that is, in the art of skilful employment of the available signs, and you will observe, Sir, by the small enclosure [on determinants] that Vieta and Descartes have not known all the mysteries.}} He refined his criteria for good notation over time and came to realize the value of "adopting symbolisms which could be set up in a line like ordinary type, without the need of widening the spaces between lines to make room for symbols with sprawling parts."<ref>{{harvnb|Cajori|1993|loc=Vol. II, p. 184}}</ref> For instance, in his early works he heavily used a [[vinculum (symbol)|vinculum]] to indicate grouping of symbols, but later he introduced the idea of using pairs of parentheses for this purpose, thus appeasing the typesetters who no longer had to widen the spaces between lines on a page and making the pages look more attractive.<ref>{{harvnb|Mazur|2014|loc=pp. 167-168}}</ref> Many of the over 200 new symbols introduced by Leibniz are still in use today.<ref>{{harvnb|Mazur|2014|loc=p. 167}}</ref> Besides the differentials {{mvar|dx}}, {{mvar|dy}} and the integral sign ( ∫ ) already mentioned, he also introduced the colon (:) for division, the middle dot (⋅) for multiplication, the geometric signs for similar (~) and congruence (≅), the use of [[Robert Recorde|Recorde's]] equal sign (=) for proportions (replacing [[William Oughtred|Oughtred's]] '''::''' notation) and the double-suffix{{cfn|date=October 2022}} notation for determinants.<ref name="Cajori185" />
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