COMMENTARY ON NEWTON’S *ARITHMETICA UNIVERSALIS.* FIRST EDITION.

### MACLAURIN, Colin (1698–1746)

### A treatise of algebra , in three parts ... to which is added an appendix, concerning the general properties of geometrical lines

London: printed for A. Millar, and J. Nourse, 1748

8vo: A^{8} (–A8) B–[2]D^{8} [2]E^{8} ([2]E8 +1), 224 leaves, pp. xiv 366 [2] 65 [1].

12 folding engraved plates, Tab. I–XII, (inserted in the second sequence of pagination according to the page numbers engraved on the plates).

*Condition:* 206 x 132mm. Slightly browned at the beginning and end.

*Binding:* Contemporary calf, spine with double fillets and small lozenge in each compartment, orange morocco lettering piece. Rubbed but sound.

*Provenance:* John Hamilton, signature dated Nov. 1756 on title; booklabel of P. G. Lowe (twentieth-century).

First edition.

*Bibliography:* ESTC t93641; Wallis *British mathematics* 713MAC48T; not in Babson or Wallis *Newton*.

An important commentary on Newton's *Arithmetica universalis*, reproducing some sections verbatim. It was probably edited by Patrick Murdoch, editor of Maclaurin's other important posthumous work, *An account of Sir Isaac Newton's philosophical discoveries* published in the same year. At least part had been written in 1726 for Maclaurin's lectures as Professor of Mathematics at Edinburgh University.

The appendix in Latin, illustrated with the plates of diagrams, is based on Newton's ‘Enumeratio linearum tertii ordinis’, first published at the end of the *Opticks* (1704), an important study of cubic curves and ‘in some ways … the most original of all Newton's mathematical work...’ (Gjertsen pp. 187–8).

Dedicated to the Archbishop of Canterbury.