Being alone doesn't make you solitary. Being solitary is feeling helpless. You can be surrounded by people and still feel solitary. You can be truly alone and not feel solitary at all. When we lose a brother, son, or friend we relied on, we say we're left solitary. This happens even in Rome, surrounded by crowds, living among many people, even with lots of slaves around. Someone who is solitary feels helpless and vulnerable to those who want to hurt them. That's why we feel most lonely when traveling and we run into robbers. It's not seeing another human being that removes solitude. It's seeing someone who is trustworthy, decent, and willing to help us.
Solitude is a certain condition of a helpless man. For because a man is alone, he is not for that reason also solitary; just as though a man is among numbers, he is not therefore not solitary. When then we have lost either a brother, or a son, or a friend on whom we were accustomed to repose, we say that we are left solitary, though we are often in Rome, though such a crowd meet us, though so many live in the same place, and sometimes we have a great number of slaves. For the man who is solitary, as it is conceived, is considered to be a helpless person and exposed to those who wish to harm him. For this reason when we travel, then especially do we say that we are lonely when we fall among robbers, for it is not the sight of a human creature which removes us from solitude, but the sight of one who is faithful and modest and helpful to us.