nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqknzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqaufa4k (nprofile…fa4k) I think this stackexchange question can be read as someone wondering about precisely your "quote", though it takes a little work to make a good choice of B.
https://math.stackexchange.com/questions/3333241/motivation-for-defining-a-tangent-vector-as-an-equivalence-class-of-curves