It means that the time signature alternates every measure, but rather than writing in all those changes, they wrote it like that. The first measure will be in 4/4, the second in 3/2, the third in 4/4, the fourth in 3/2, etc. At least that's what I'm guessing without actually seeing the music. Would that make sense with the number of beats in each measure?

Ooohhhh...Yes, renaissance/medieval type music used very different notation from what we're used to today. I'm afraid I'm no expert on music from that era, so I can't be much more help, at least without seeing the sheet music. As for that one without a time signature, that's not terribly uncommon. I've performed a couple of pieces like that before, though generally I don't seem to care for them.

I have been reluctaant to respond because I don't have a clue what
43
42
is there for.
Music in 1300 used Mensural notation which was basically written in Longa and Breves. Which today the Longa would be the equivalent of the double whole note (It exists still and it still looks square). The brev is todays wholoe note. So Ala brev meant, "In the speed of the Breve"

Music was divided between metered

http://en.wikipedia.org/wiki/Rhythmic_mode
and chants If I remember correctly.
See:
http://en.wikipedia.org/wiki/Gregorian_chant

for a photo of early music.

The metered music used specific symbols such as the C (which we now call "Common Time" ) The C meant nothing of the word common. It meant a meter which had 4 beats and each beat was divisible by 2. Another example would have been a O with a dot in the middle. This time signature was considered perfect in a religious sense and was in essence 3 beats divisible by 3 or 9/8. An example would be Bach's Jesu, Joy of Man's desiring. The meter that Bach choose may reperesent the trinity (3)with in the trinity (3). The perfect time sig. for God.

oh my gosh!!!!!! YOU LEARN SOMETHING NEW EVERYDAY!!!! that's wierd that they even HAVE that in music.........sorry i don't have a clue what it means and thanks to Flutist06 you now know....i couldn't have guessed for my life.....honestly

"Lo how a rose e're blooming"
is a very common old German Christmas tune.

http://www.cyberhymnal.org/htm/l/h/lhowrose.htm

MIDI arrangement of the tune at that link.

<Added>

The time signature in question "may have been" meant to mean:
4
-
4 and then

3
-
2

so that it alternates between 4/4 and 3/2 meters.