In 1248 he returned to Cologne with Albertus, and was appointed second lecturer and magister studentium.
Owing to the fame of this work, he is mentioned by Dante as the Magister sex principiorum.
In 385 he was appointed master of the soldiery (magister militum) in Thrace, and shortly afterwards directed energetic campaigns in Britain against Picts, Scots and Saxons, and along the Rhine against other barbarians.
The methods which Leonardo made use of in solving those problems fill the Liber quadratorum, the Flos, and a Letter to Magister Theodore.
In the Letter to Magister Theodore indeterminate problems are chiefly worked, and Leonardo hints at his being able to solve by a general method any problem of this kind not exceeding the first degree.