Composer John Dowland (1563-1626) lived in the time of the long reign of Elizabeth I, Queen of England and Ireland. In fact he was a contemporary of Shakespeare. Dowland is famous especially for his songs and works for lute. I suppose you could call him the pre-eminent Renaissance singer/songwriter. Much of his music was printed, but the printing of music was somewhat new at the time, and copies of manuscripts and personal copies of music were still prevalent. One of his compositions in the form of a puzzle canon per tonos is found in a "book of friends", or Album Amicorum, belonging to Johannes Cellarius. In this case, the canon falls by a tone with each repetition.
You can see that in writing the canon out in its enigmatic form Dowland did not have a straight edge, and the resulting awkwardly sized staves led to inconsistent note head sizes.
The canon is solved at the fourth above. Notice that, as with other modulating canons, the direct (squiggle) at the end of the music indicates that the next note will be a step below the first note causing the canon to fall by a step with each repetition.
The fun thing about such canons, and what makes them ideal for friends, is the challenge of playing them. In a duo such as this, who would be the first to fail? It would clearly be worth a laugh in order to find out.
The challenging thing about writing them is to keep the modulation from standing out too much. For this reason, brief modulating canons are more tricky, but no matter the length, the modulation must be accomplished artfully, avoiding a simple and sudden transposition. If accomplished well, it will be done with a pivot: a period of time where the music could reasonably be claimed to be in the old key, but just as reasonably be claimed to be in the new key. This is done by avoiding the differences between the keys for a time, so that they do not clash, even by juxtaposition or memory.
Keys a step apart are relatively distant from one another, but not radically so. In order to bridge the distance between these keys, Dowland (and the other composers of modulating canons) used the key that falls in between the two. This is best visualized using a circle of fifths.
The Fuga is notated in D minor, but the answer is in G a fifth away. Falling a full tone would move the key to C minor, but the answer bridges these two keys: instead of jumping two keys from D, counterclockwise (anticlockwise) to C, the key of G is introduced.
And this makes good sense when considering the notes involved. Let's think of the notes surrounding the circle of fifths as representing minor keys.
The diatonic notes in the key of D minor differ from those in G minor only by one note, and the same degree of difference holds between G minor and C minor. The two degrees of separation between D minor, the initial leader and its first repetition is thus tempered as the follower is introduced a full tone lower, from D to C. Instead of two notes appearing suddenly, there was time for the E-natural that appears in D minor to be replaced by E-flat (key of G minor), before the note A-flat is introduced when the key of C minor prevails.
Incidentally, the term Fugue or Fuga in the Renaissance is used in a much more general way than it is in the Baroque era, when it becomes a certain type of composition. Here it means "imitative piece" or "canon". It also implies that the imitation is real as opposed to tonal.
I think the words below are "Jo: Dolandi [Dowland] di Lachrimae", meaning John Dowland of the pieces (pavans, etc.) entitled "Lachrimae" (published in 1604, though written earlier). And the meaning of "in his own hand" is clear enough, as this is his autograph.