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Girdle of Andromeda, in the Months of February and March, 1664. the other in Germany in Capricorne, about Saturne in the head of 5agittary, during the Months of September and October, 1665. 2ly, With an Advertisement of what he has done in that important Work for the Advancement of Astronomy, the due Restitution of the Fixt Stars, vid. That he has almost finish't it, himself alone, without trusting to any other mans labour, that was not directed by him.
The Second Part of this Book (the Mantissa to the Prodromus Cometicus) endeavours to justifie the Authors Observations touching the former Comet, excepted against by M. Auzout, in several particulars, as 1. That it had not pass'd to the First, but Second Star in Aries, and had mov'd in quite another Line, than He had described. 2. That its proper motion about the end of January and the beginning of February, 1665. had not been rightly assigned. 3. That the Bignesse of its Diameter had not been truly delivered; Nor 4. The Faces of its Head in due manner represented.
To all which the Author endeavors to answer: 1. By delivering all his Observations of that Comet, thereby to shew, what care and diligence he had used, particularly to make out, how great its Diurnal motion had been, in what proportion, and how far, it decreased, and where and in what degree it increased again: Which being, as he conceives, duly and exactly deduced, and demonstrated, he esteems it afterwards to be easie for every one, versed in these matters, certainly to collect and to judge, what way the Comet, after it became invisible to the naked Eye, and could be no longer observed with Sextants and Quadrants, had taken, and what Line it had described. 2, By subjecting all those Observations, with great diligence and labour, to a rigid Calculus, thereby to obtain, for every day, the Longitudes, Latitudes, Right Ascensions, Declinations, Proper motion, Angle of the Ecliptick and the Æquator, and the Nodes of that Comet; for the construction of an Ephemerides of its whole Motion. From all which he pretends to prove, that he has not erred in his Observation of February 18. nor been prepossest by any Hypothesis, nor deluded by any Fixt Star, as M. Auzout thinketh, but that near the First Star' of Aries there then appear'd a Phænomenon, most like to that Comet, that was seen some dayes before, if compared with the Observations made thereof Febr. 12, 13, 14. Though he will not hitherto positively determine, whether that Phænomenon, which appear'd to him February 18. was
