Brandenburg was brought in afterward almost by force.

The Duke of Saxony mustered his forces under the walls of Leipsic,
and I having returned to Leipsic, two days before, saw them pass the
review. The duke, gallantly mounted, rode through the ranks, attended
by his field-marshal Arnheim, and seemed mighty well pleased with
them, and indeed the troops made a very fine appearance; but I that
had seen Tilly's army and his old weather-beaten soldiers, whose
discipline and exercises were so exact, and their courage so often
tried, could not look on the Saxon army without some concern for them
when I considered who they had to deal with. Tilly's men were rugged
surly fellows, their faces had an air of hardy courage, mangled with
wounds and scars, their armour showed the bruises of musket bullets,
and the rust of the winter storms. I observed of them their clothes
were always dirty, but their arms were clean and bright; they were
used to camp in the open fields, and sleep in the frosts and rain;
their horses were strong and hardy like themselves, and well taught
their exercises; the soldiers knew their business so exactly that
general orders were enough; every private man was fit to command, and
their wheelings, marchings, counter-marchings and exercise were done
with such order and readiness, that the distinct words of command
were hardly of any use among them; they were flushed with victory, and
hardly knew what it was to fly.

There had passed some messages between Tilly and the duke, and he gave
always such ambiguous answers as he thought might serve to gain time;
but Tilly was not to be put off with words, and drawing his army
towards Saxony, sends four propositions to him to sign, and demands an
immediate reply. The propositions were positive.