Final answer:
Brutus's point is that people actively seek recognition and glory through acknowledgment of their deeds and contributions, to which even generals and philosophers are not immune.
Step-by-step explanation:
The summary of Brutus's point in lines 15–28 is that certain individuals seek not only recognition but also actively play a role in the pursuit of glory and honor, whether they are poets, philosophers, generals, or statesmen. They go as far as inscribing their names on their works and temples to ensure acknowledgement for their deeds. Brutus argues that many, including generals and esteemed citizens, have respected poets and contributed to the arts, implying that such acts of recognition and patronage are honorable and should be continued. This pursuit of praise is seen as natural and particularly compelling for the best of men, driving them toward glory.