A mathematical dictionary seems like a good place to start looking to get an idea of what mathematics was in Early Modern Europe. The first such dictionary was by Joseph Moxon (1617-1700), entitled:

*Mathematicks made Easie Or, A Mathematical DICTIONARY explaining The Terms of Art, and Difficult Phrases used in Arithmetick, Geometry, Astronomy, Astrology, and other Mathematical Sciences : Wherein the true Meaning of the word is Rendred, the Nature of the Things signified Discussed, and (where Need requires) Illustrated with apt Figures and Diagrams : with an APPENDIX, exactly containing the Quantities of all sorts of Weights and Measures: The Characters and Meaning of the Marks, Symbols, or Abbreviations commonly used in Algebra. And sundry other Observables.*

This was first published in London in 1679. Eells (1961) gives an account of the 1692 edition. The first mathematical dictionary in French was by Jacques Ozanam (1640-1718) published in 1691 under the title:

*Dictionnaire mathématique, ou, Idée generale des mathematiques : Dans lequel l’on trouve, outre les Termes de cette science, plusieurs Termes des Arts & des autres sciences; Avec les raisonnemens qui conduisent peu à peu l’ésprit à une connoissance universelle des mathematiques.*

Jacques Ozanam,* Dictionnaire mathematique, ou, Idée generale des mathematiques*

(Paris, 1691), p. 69.

In 1702, James Raphson (1668-1715) published an abridged English translation of Ozanam’s *Dictionnaire mathématique* entitled:

*A Mathematical Dictionary: or, a Compendious Explication of all Mathematical Terms, Abridg’d from Monsieur Ozanam, and Others. With a Translation of his Preface; and an Addition of several easie and useful Abstracts; as plain Trigonometry, Mechanicks, the first Properties of the three Conick Sections, &c. To which is added, an Appendix, containing the Quantities of all Sorts of Weights and Measures; the Explanation of the Characters used in Algebra. Also the Definition and Use of the Principal Mathematical Instruments, and the Instruments themselves curiously Engraven on Copper.*

Ozanam’s dictionary is in the Edward Worth Library. It is hard not to be struck by the breadth of purpose in his dictionary (quite apart from its relatively succinct title) – with the rationale that leads the mind little by little to a universal knowledge of mathematics! The contents of his dictionary are broad indeed; here is an abridged version of the contents (with some headings grouped when dealing with a common theme): The general idea of mathematics, Arithmetic, Algebra, Geometry, Cosmography, Astronomy, Geography, Navigation, Celestial bodies, Optics, Painting, Mechanics, Statics & hydrostatics, Architecture, Music. Roughly speaking, this appears to be a development of the quadrivium which has its origins in late antiquity: arithmetic, geometry, astronomy and music.

Jacques Ozanam, *Dictionnaire mathematique, ou, Idée generale des mathematiques*

(Paris, 1691), p. 110.

This page is clearly from the chapter on geometry, summarizing one, two and three dimensional shapes. The earlier illustration (p. 69), treating the problem of measuring an inaccessible height, AB, by means of a plane mirror, is from the chapter on algebra. Here the two pairs of similar triangles allow the simple derivation of equations that can be solved algebraically to find AB. Much of the algebra in this section is effectively analytic geometry in the spirit of Descartes, with some treatment of polynomial equations towards the end. The final illustration is from the first chapter on the general idea of mathematics. It shows the problem of finding a point, D, in a given triangle, ABC, that is equidistant from A and a point, E, on AC, and so that (i) DE is parallel to BC and (ii) F, the point where the extension of ED meets AB, is equidistant from B and D. This problem follows a ‘lemma’ (or little theorem) that gives conditions for which the ratio of HI to AF is equal to the ratio of BF to DF.

Jacques Ozanam, *Dictionnaire mathematique, ou, Idée generale des mathematiques*

(Paris, 1691), p. 11.

**Sources**

Eells, W. C., The first mathematical dictionary, *The Mathematics Teacher*, 54 (4) (1961), 255-260.

O’Connor, J. J. and Robertson E. F., Jacques Ozanam,* MacTutor History of Mathematics*, (University of St Andrews, Scotland, February 2002).

O’Connor, J. J. and Robertson E. F., Joseph Raphson, *MacTutor History of Mathematics*, (University of St Andrews, Scotland, February 1996).

Raphson, J. and Ozanam, J., *A Mathematical Dictionary: Or; A Compendious Explication of All Mathematical Terms, Abridged …* (London, 1702).

**Text:** Maurice OReilly and Eimear Mullan.