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IV. On the Use of Negative Quantities in the Solution of Problems by Algebraic Equations

Published online by Cambridge University Press:  17 January 2013

William Greenfield
William Greenfield
Affiliation:
Minister of St Andrew's Church, and Professer of Rhetoric in theUniversity, of Edinburgh.
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Extract

By the introduction of letters into algebra, to denote all the quantities, both known and unknown, involved in an equation, this very important advantage was gained, that the final equation exhibited both a general rule for the solution of all similar problems, and also the limitations within which such problems were possible.

Type
Papers Read Before the Society
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 1 , Issue 2 , 1788 , pp. 131 - 145
Copyright
Copyright © Royal Society of Edinburgh 1788

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References

page 132 note * I Have not been able to procure the book; but the following passage, quoted by Dr Horseley, seems to warrant what has been asserted: “Jusques icy nous n'avons encore” expliqué à quoy servent les solutions par moins, quand il y en a. La solution par “moins s'explique en geometrie en retrogradant, et le moins recule là où le + avance.” And, after giving an instance, he adds; “Et ainsi saudra + il entendre de toutes solutions” par moins; qui est une chose de consequence en geometrie incognue auparavant.” Horseley's Newton, vol. 1. p. 171. note (u).

page 132 note † Montucla Hist. de Math. vol. 2. p. 85.

page 132 note ‡ Montucla Hist. de Math. vol. 2. p. 82. & 84.

page 136 note * Dissert. on the Neg. Sign, p. 34.