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. 1920 Excerpt: ...1673 constructs the so-called characteristic triangle, but does not give Leibniz's figure in connection. This figure should have been given; for the figure given in October 1674 is not the characteristic triangle as given by Leibniz in the "postscript" ( 1), or the Historia ( 2), but it is the Pascal diagram (assuming ...
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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. 1920 Excerpt: ...1673 constructs the so-called characteristic triangle, but does not give Leibniz's figure in connection. This figure should have been given; for the figure given in October 1674 is not the characteristic triangle as given by Leibniz in the "postscript" ( 1), or the Historia ( 2), but it is the Pascal diagram (assuming that the figure given by Cantor is the correct one). It would be useful to know the date at which Leibniz drops the Pascal diagram in favor of one or other of the Barrow diagrams. It is to be noticed at this date that Leibniz uses one infinitesimal only, and verifies that the method of Descartes comes out correctly in the simple case of the parabola; but he is not satisfied with the generality of the method of neglecting the vanishing quantities. Again, the second manuscript of October 1674 appears to be immensely important; especially as it contains the groundwork of some of the later manuscripts. Judging by the little that is given of it, it would seem to be most desirable that fuller extracts, at least, should have been given. It is a matter for remark that this manuscript is a long essay on series. Can this possibly have had anything to do with the fact that it is not given in full? MANUSCRIPTS OF THE PERIOD 1676, 1677, AND A LATER UNDATED MANUSCRIPT. 11-15. Between the date of the manuscript last considered and the one which follows there is a gap of seven months, for which Gerhardt does not appear to have found anything. This is very unfortunate; for in this interval Leibniz has attained to the important conclusion that the true general method of tangents is by means of differences. We saw that in November 1675 he had started to investigate more thoroughly the direct method of tangents; but the method is...
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All Editions of The Early Mathematical Manuscripts of Leibniz; Translated from the Latin Texts Published by Carl Immanuel Gerhardt with Critical and Historical Notes
