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Doc. 313.] 893
CHRONOLOGICAL ACCOUNT.
Section I. The foundation of algebra; the definition of signs,
pp. 4 to 15.
Section II. The mode of counting with letters, pp. 15 to 30.
Section III. The method of counting fractions, pp. 37 to 66.
On p. 57 the author introduces a new scale for weighing metals in
water and in the air, by which it can be shown, for instance, how
much copper is contained in gold.
Section IV. On raising the power of letters, and computing
therewith, pp. 66 to 83.
Section V. On equations, pp. 84 to 103.
Section VI. Extraction of square-roots, pp. 103 to 115.
Section VII. Raising all the roots to whatever power is
required, pp. 115 to 135.
The remaining three sections, which were to treat of the adfected
roots, the differential and integral calculus, were not finished by
Swedenborg in this treatise.
This work was most favourably noticed by the following reviews :
Acta Literaria Sueciæ, for 1720, pp. 126 to 134 ; and Neuere
Zeitungen von gelehrten Sachen auf das Jahr 1722, Part I, Leipzig,
p. 378 et seq.
Swedenborg expresses himself with respect to his "Regel
konst" as follows, "As I had some leisure hours here at Brunsbo,
I have prepared an Algebra in Swedish; and although I had no
book or other help at hand, I have tried to make it as easy and
concise as possible; it will probably not exceed six sheets in print.
I was induced to write it chiefly because so many in Lund and
Stockholm have begun to study algebra, and because I have been
requested by others to prepare it; I hope that it will be of service
to the public" (
Document 76, p. 290).
1718. (16.) Geometrica et Algebraica (Contributions to
Geometry and Algebra) ; in MS., 169 pages, 4to.
This is a treatise on higher Mathematics consisting of Section I
to IV, and Section X of Codex 86, described in Document 310.
The plan of this work, which is written in Latin, is set forth in
full on pp. 98 to 100, of Vol. II of Swedenborg’s Photo-lithographed
MSS. The author begins his work by first summing up briefly the
results taught in his " Regelkonst," and then proceeds to what he
calls the "Calculus of Exponents ;" and after treating in full concerning
equations, he shows how equations may be resolved into analogies ;
and finally he treats of his new method of finding out and demon
strating expeditiously the proportion of two geometrical magnitudes,
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