You probably got this far yourself, but here is my absolutely wild
speculative guess on why this could be 24 May 1587 on the Gregorian
calendar:
It seems fairly clear that this refers to the 24th of some month
in 1587, but it's not as clear which month this is, and whether this
is in the Gregorian or Julian calendar.
The moon symbol followed by the symbol for Taurus may indicate
"the month where the new moon was in Taurus". This is slightly
ambigious, since the new moon is was Taurus on both June 6th and May
7th, but I believe May 7th slightly is more likely for the reasons
below.
Wikipedia notes that "cerasus" is a a dated synonym of the genus
Prunus (https://en.wikipedia.org/wiki/Cerasus), which includes
cherries.
Historically, there is no "Cherry Moon" (although there are songs,
movies, and possibly more that mention it), but cherry trees are
known for their flowers, so this may be a reference to the Full
Flower Moon of May:
http://farmersalmanac.com/full-moon-names/
- The word "gexia" translates to "Your Mightiness" in Chinese:
https://translate.google.com/#auto/en/gexia
but I'm pretty sure this is red herring, since the paper doesn't
appear to be in Chinese, and I'm not sure Chinese transliteration even
existed at the time. However, it would fit in nicely.
So this could be saying "the full cherry (flower) moon occurs on
24 May 1587". Unfortunately, the actual full moon occurs late on the
22nd GMT, so the 24th is a bit of a stretch even allowing for the
16th century equivalent of "time zones"
The Gregorian calendar reform occurred in 1582. Many countries
didn't adopt it until much later, but the text appears to be in a
Latin-based language (ie, a Romance language), and countries like
this were quick to switch to the Gregorian calendar:
https://en.wikipedia.org/wiki/Adoption_of_the_Gregorian_calendar#Adoption_in_Catholic_countries
- If this is 24 May 1587 in the Julian calendar, it would be 10 days
later, 3 Jun 1587, in the Gregorian calendar. This date seems less
likely, since there is no full moon on that date, though there is
almost a new moon in Taurus, so maybe.
So why would the author write "month of moon in Taurus" instead of the
actual month name? It's possible he was trying to be careful, since
the months would be different in the many countries still using the
Julian calendar.
Of course, it may just be a reference to the lunar eclipse of 24 Mar 1587:
http://eclipsewise.com/lunar/LEprime/1501-1600/LE1587Mar24Tprime.html