The Polish astronomer Johannes Hevelius had invented the polemoscope in the 1630s and described it in his book about the moon, Selenographia (1647). The polemoscope is described by the OED as 'a telescope or perspective glass fitted with a mirror set at an angle to the line of vision, for viewing objects not directly before the eye'. The name (from a Greek stem meaning war) reflects the potential military uses to which Hevelius thought the instrument could be put, although Robert Hooke casts doubt on this.
In this letter we see Hooke in his technical element, advising the Somerset clergyman John Beale on the use of microscopes and telescopes and adjusting his instruments for him. The planet Venus, being visible to the naked eye, was a particularly good subject for the amateur astronomer, particularly when it was nearest the earth at the perigee of its orbit. Viewed from the earth, Venus exhibits similar phases to those of the moon - hence the reference to the 'horns' of the plant's crescent phase.