This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 Excerpt: ...with vectors in the plane of the paper before us, the relation of a vector with currency toward the right to a perpendicular horizontally upward vector is assigned a positive neomonic value while the relation of the vector with right hand currency to a perpendicular horizontally downward vector is assigned a negative ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 Excerpt: ...with vectors in the plane of the paper before us, the relation of a vector with currency toward the right to a perpendicular horizontally upward vector is assigned a positive neomonic value while the relation of the vector with right hand currency to a perpendicular horizontally downward vector is assigned a negative neomonic value. But this could easily be reversed by mere convention, relations of the former type being, at the option of the mathematician, made positive and those of the latter made negative. In Quaternions the arbitrary nature of the classification of neomonic abstract quantities as positive and negative is even more obvious. For Hamilton adopted as positive direction of rotation that which is followed by the hands of a clock, while Tait and later quaternionists took the reverse direction of rotation as positive. And this amounts to saying that the relations (quaternions) which Hamilton designated as of value +i and +j, and classed as positive, were by Tait classed as negative, and had their values represented by--i and--j respectively; and vice versa Hamilton's negative quaternions of value--i and--j were by Tait made positive, and given the value symbols +i and +.7.1 In general, with each set of abstract nonzeroes that goes to make up a neomonic kind, the mathematician has, up to the time the conventions of comparison are laid down, merely two confluent and mutually contrafluent sets of quantities before him, and he can at his will so lay down these conventions as to make either set positive and the other set negative. As to the protomonic abstract varieties, the case is somewhat different. If we adhere to the rule of laying down the conventions of comparison between the non-zeroes of each positive variety in such manner that two of these...
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Seller's Description:
Very Good. The Open Court Publishing Company, 1916. Stated First Edition; signed and inscribed by author Edward Landis on ffep; cover/spine ends lightly rubbed/bumped; edges lightly soiled/bumped, quite age toned; ffep lightly soiled; interior lightly age toned throughout; binding tight; cover, edges, and interior intact and clean except as noted. Signed by Author. First Edition. Hard Cover. Very Good.
