Download PDF by Arthur Cayley: An elementary treatise on elliptic functions

By Arthur Cayley

This quantity is made from electronic pictures from the Cornell college Library historic arithmetic Monographs assortment.

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Sample text

De Morgan pointed to some forms of inference which lay 30 CHAPTER 2 PRELUDES: TO 1870 outside the syllogistic ambit. ‘For example’, a well-remembered one, ‘ ‘‘man is animal, therefore the head of a man is the head of an animal’’ is an inference, but not syllogistic. And it is not mere substitution of identity’ Ž 1847a, 114.. To cover such cases he offered the additional rule ‘For every term used universally less may be substituted, and for every term used particularly, more’ Žp. 115.. While his treatment was not fully satisfactory, his modifications can be cast in a sound form ŽSanchez Valeria 1997a..

If a function f satisfied the property f Ž x q y q иии . s f Ž x . q f Ž y . 2. then f ‘will be called distributi¨ e’; and if f and another function g satisfied the property f Ž g Ž x .. s g Ž f Ž x .. 3. then they ‘will be called commutati¨ e between each other’ Žp. 98.. , was not a normal procedure at the timeᎏthen he would have put forward two axioms for a general algebra. 2᎐3.. 3 This feature was reflected in the practise of several authors to use the word ‘characteristic’ to refer to the letters of the algebra, not to the functions or operators to which they referred.

220.. Compound relations were indicated by the concatenation ‘LM ’, and quantification over relations by primes such that LM X ‘signify an L of e¨ ery M ’ and L, M ‘an L of none but Ms’. The converse to L was written ‘Ly1 ’, or ‘L¨ ’ for ‘Those who dislike the mathematical symbol’;15 further, ‘Ly1 X may be read ‘‘L-¨ erse of X ’’ ’ Žp. 222.. He also proved that ‘if a compound relation be contained in another relation, w . . x the same may be said when either component is converted, and the contrary of the other component and of the compound change places’ Žp.

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An elementary treatise on elliptic functions by Arthur Cayley

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