of the Heavens. For, both the present Comet, and many others
registred in History, have entred that way, and consequently passed out of
it by the sign _Aries_, by which also many have entred.

I did found my _Hypothesis_ upon three Observations only, _viz._ those of
the 22, 26, and 31. of _December_. Nor have I done, as some have fancied of
me, who having been able to observe the Comet, the 27, 28, 29, 30, and 31.
of _December_, and to see the diminution of its motion, have judged, that I
had only determined that diminution for the time to come, conform to the
augmentation thereof in time passed until the 29. of _December_. For
_January_ 1. (on which day I composed my _Ephemerides_) I knew not (nor any
person here) that the motion of the Comet did diminish; but on the
contrary, most men believed, it was not the same Comet. But Signior
_Cassini_ knows very well, that that was not necessary, seeing that two
portions of a _Tangent_ being given, and the _Angles_ answering thereunto,
'tis easie to find the position and magnitude of its Circle. The reason,
which I think the true one, of the diminution of its Motion in Longitude,
and of its Retrogradation, by me conjectured in my _Ephemerides_, I began
to be assured of, _Febr._ 10. For until the sixth, the Comet had alwaies
advanced, as Signior _Cassini_ also hath very well noted: but after that
day, I found that it returned in augmenting alwaies its Latitude. And I
have constantly observed it, until _March_ 8. between many Stars, which
must be the same with these mentioned by _Cassini_, whereof the number was
so great, that I think, I saw of them _March_ 6. with one _Aperture_ of my
Glass, more than 40. or 50. and especially, above the head of _Aries_; but
I did not particularly note the scituation of more than 12. or 15; amongst
which I have observed the position of the Comet since _January_ 28. every
day, when the weather did permit, _viz._ _January_ 29. _February_ 3, 6, 10,
17, 19, 24, 26, 27. and _March_ 6, {20} 7, 8. I left it on _March_ 8. at
the 18. of the Horn of _Aries_, almost in the same latitude: and I am apt
to believe, it will be Eclipsed, which I wish I may be able to observe this
evening, if it be not already passed.

If Signior _Cassini_ hath observed it on those daies that I have, he will
be glad to find the conformity of our Observations. I shall only add, that
on _February_ 3. we were surprized, to see the Comet again much brighter
than ordinary, and with a