FLAMSTEED, John (1646-1719). The Doctrine of the Sphere, Grounded on the Motion of the Earth, and the Antient Pythagorean or Copernican System of the World. London: A. Godbid & J. Playford, 1680. 4to (231 x 174 mm). [12], 104 pp. Six engraved plates, 4 folding, letterpress tables. Modern half calf. Condition: lower corner of E2 torn away causing some text loss, caption of 1st plate cropped, plate 4 with marginal reinforcement, plate 5 marginally soiled & with small tear at top, first 7 leaves chipped at top, marginal staining & soiling throughout. Provenance: manuscript correctionsin two hands, one possibly authorial, the other 18th-century. first edition of flamsteed's first work, published as part of Jonas Moore's posthumously published New Systeme of the Mathematicks (1681). The work includes an improved version of Jeremiah Horrocks' calculations of the motions of the moon, which Flamsteed had helped Horrocks prepare for publication in 1673. This copy bears several interlinear and marginal corrections which may be the author's own. These interlinear notes correct both textual and numerical errors, and include a few corrections to the tables at end. These small corrections to text, equations or tables are apparently to be distinguished from the more copious marginalia, in a different, somewhat later hand, including mathematical calculations, notes on the calculation of distances, captions on the plates, and marginal references from the text to figures in the plates. The edition itself is rare. The only other copy to appear at auction in the last 30 years, the Macclesfield copy, sold in 2004, was also annotated by the author (hammer price £16,000). Wing F1137; Houzeau & Lancaster 12077.