In the following book, please look at equation 3.16. Why are the components of the tangent vector given by ui = dxi/dt? I understand the velocity components would be dxi/dt and the velocity vector would be a tangent vector. Is that the same reasoning the author uses? The book is normally crystal clear, but, this specific discussion confused me. https://books.google.com/books?id=7zFalCF_LiEC&pg=PA48&lpg=PA48&dq=tangent+vector+parabola+dx/dt&source=bl&ots=Q2m0RBTbkI&sig=moW1rwceNUEop-SkG5rLfkeAZhY&hl=en&sa=X&ved=0ahUKEwjrgee4qKbMAhWCw4MKHeE7D3gQ6AEIJTAC#v=onepage&q=tangent vector parabola dx/dt&f=false Thanks in advance for your help!