Sämtliche Schriften und Briefe. Reihe 3. Mathematischer, naturwissenschaftlicher und technischer Briefwechsel. Band 3: 1680 – Juni 1683. Herausgegeben von Herbert Breger.

*(Latin, French, German)*Zbl 0743.01033
Berlin: Akademie-Verlag (ISBN 3-05-000766-4). lx, 896 S. (1991).

This excellent critical edition comprises three and a half years of Leibniz’s mathematical, scientifical and technical correspondence (1680- 1683). It publishes at the very beginning two supplements belonging still to the preceding year 1679 and volume of this edition. While 344 letters, documents or supplements to letters are published, mainly for the first time, the existence of further 140 letters is reconstructed by allusions so that the edition proper comprehends 484 items. 60 correspondents and four unknown authors are involved. Thirteen items are neither written by Leibniz nor sent to him, but are closely connected with letters exchanged by him. The four correspondences with J. D. Crafft, J. J. Ferguson, E. Mariotte and E. W. v. Tschirnhaus fill approximately half of the volume.

The editor Breger added a very valuable and helpful introduction which contains surveys of the nine principal subjects which are dealt with within this volume: 1. physics (reduction of mechanics to geometry, acoustics, magnetic declination), 2. Leibniz’s activities in the Harz mountains (windmills, geology, mineralogy), 3. activities for the Court in Hanover, personal plans, 4. the organization of science, 5. economic and technical projects which are mainly discussed between Elers, Crafft and Leibniz, 6. chemistry and alchemy (phosphorus), 7. medicine, 8. philosophy (characteristic, art of inventing, proofs for God’s existence), 9. mathematics: Though it does not play the same important role as in the two preceding volumes, many interesting mathematical topics are dealt with. The following ten correspondents have to be mentioned in this respect: D. Clüver (reciprocal figurated numbers, calculating machine characteristic), Fr. de la Chaise (quadrature of the circle), J. J. Ferguson (number theory, series, determinants, arithmetical quadrature of the circle, Alhazen’s problem, algebraic equations, curves), Chr. Huygens (calculus), A. A. Kochański (quadrature of the circle), S. de la Loubère (ratios, continued fractions), A. Magliabecchi (elementary geometry), E. Mariotte (catacaustics, curves), Chr. Pfautz (exponential equations, calculations of annuities), E. W. v. Tschirnhaus (curves, tangent constructions).

The copiousness of information presented in this volume, its high editorial standard cannot be adequately appreciated in this short review. Like in all other volumes of this fundamental edition of Leibniz’s letters and writings there are several indispensable indices, that is of correspondents, of places where the letters were sent off, persons, of writings belonging to Leibnizian times, subjects, abbreviations, chemical signs, corrections.

The editor Breger added a very valuable and helpful introduction which contains surveys of the nine principal subjects which are dealt with within this volume: 1. physics (reduction of mechanics to geometry, acoustics, magnetic declination), 2. Leibniz’s activities in the Harz mountains (windmills, geology, mineralogy), 3. activities for the Court in Hanover, personal plans, 4. the organization of science, 5. economic and technical projects which are mainly discussed between Elers, Crafft and Leibniz, 6. chemistry and alchemy (phosphorus), 7. medicine, 8. philosophy (characteristic, art of inventing, proofs for God’s existence), 9. mathematics: Though it does not play the same important role as in the two preceding volumes, many interesting mathematical topics are dealt with. The following ten correspondents have to be mentioned in this respect: D. Clüver (reciprocal figurated numbers, calculating machine characteristic), Fr. de la Chaise (quadrature of the circle), J. J. Ferguson (number theory, series, determinants, arithmetical quadrature of the circle, Alhazen’s problem, algebraic equations, curves), Chr. Huygens (calculus), A. A. Kochański (quadrature of the circle), S. de la Loubère (ratios, continued fractions), A. Magliabecchi (elementary geometry), E. Mariotte (catacaustics, curves), Chr. Pfautz (exponential equations, calculations of annuities), E. W. v. Tschirnhaus (curves, tangent constructions).

The copiousness of information presented in this volume, its high editorial standard cannot be adequately appreciated in this short review. Like in all other volumes of this fundamental edition of Leibniz’s letters and writings there are several indispensable indices, that is of correspondents, of places where the letters were sent off, persons, of writings belonging to Leibnizian times, subjects, abbreviations, chemical signs, corrections.

Reviewer: E.Knobloch (Berlin)

##### MSC:

01A75 | Collected or selected works; reprintings or translations of classics |

01A45 | History of mathematics in the 17th century |