Thomas Harriot's "Artis analyticae praxis" is an essential work in
the history of algebra. To some extent it is a development work of
Viete, who was among the first to use literal symbols to stand for
known and unknown quantities. But it was Harriot who took the
crucial step of creating an entirely symbolic algebra, so that
reasoning could be reduced to a quasi-mechanical manipulation of
symbols. Although his algebra was still limited in scope (he
insisted. for example, on strict homogeneity, so only terms of the
same powers could be added or equated to one another), it is
recognizably modern. Although Harriot's book was highly influential
in the development of analysis in England before Newton, it has
recently become clear that the posthumously published Praxis
contains only an incomplete account of Harriot's achievement: his
editor substantially rearranged the work before publishing it, and
omitted sections that were apparently beyond his comprehension,
such as negative and complex roots of equations. The commentary
included with the translation attempts to restore the Praxis to the
state of Harriot's draft. Basing their work on manuscripts in the
British Library, Pentworth House, and Lambeth Palace, the
commentary contains some of Harriot's most novel and advanced
mathematics, very little of which has been published in the past.
It will provide the basis for a reassessment of the development of
algebra.
The present work is the first ever English translation of the
original text of Thomas Harriota (TM)s Artis Analyticae Praxis,
first published in 1631 in Latin. Thomas Harriota (TM)s Praxis is
an essential work in the history of algebra. Even though Harriota
(TM)s contemporary, Viete, was among the first to use literal
symbols to stand for known and unknown quantities, it was Harriott
who took the crucial step of creating an entirely symbolic algebra.
This allowed reasoning to be reduced to a quasi-mechanical
manipulation of symbols. Although Harriota (TM)s algebra was still
limited in scope (he insisted, for example, on strict homogeneity,
so only terms of the same powers could be added or equated to one
another), it is recognizably modern.
While Harriota (TM)s book was highly influential in the
development of analysis in England before Newton, it has recently
become clear that the posthumously published Praxis contains only
an incomplete account of Harriota (TM)s achievement: his editor
substantially rearranged the work before publishing it, and omitted
sections that were apparently beyond comprehension, such as
negative and complex roots of equations.
The commentary included with this translation relates the
contents of the Praxis to the corresponding pages in his manuscript
papers, which enables much of Harriot's most novel and advanced
mathematics to be explored. This publication will become an
important contribution to the history of mathematics, and it will
provide the basis for a reassessment of the development of
algebra.
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