Although texts such as Berg et al. tend to refer to inorganic phosphate, $\ce{P_i}$, as orthophosphate ($\ce{PO4^{3-}}$), the term inorganic phosphate is used because in aqueous solution at pH 7.6 several phosphate species exist, the predominant one being $\ce{HPO4^{2-}}$. If this is regarded as $\ce{P_i}$, then it is the source of the $\ce{H^{+}}$, and the equation balances.

Although texts such as Berg et al. tend to refer to inorganic phosphate, $\ce{P_i}$, as orthophosphate ($\ce{PO4^{3-}}$), the term inorganic phosphate is used because in aqueous solution at pH 7.6 several phosphate species exist, the predominant one being $\ce{HPO4^{2-}}$. If this is regarded as $\ce{P_i}$, then it is the source of the $\ce{H^{+}}$, and the equation balances.

Note added by David:

On checking I find, in contrast to Berg, Lehninger’s book defines $\ce{P_i}$ as monohydrogen phosphate ($\ce{HPO4^{2-}}$), and Fersht actually writes the equation of the reaction (16-1) with $\ce{HPO4^{2-}}$ rather than $\ce{P_i}$.

Inorganic phosphate (PO₄) is not soluble in water. In cells, it exists as a mixture of hydrogen phosphate (HPO₄) and dihydrogen phosphate (H₂PO₄), both much more soluable. That's where the extra H+ comes from. For simplicity's sake, inorganic phosphate is just indicated as P_i but that doesn't give the exact form it takes in the cell.

_Phosphate

Although texts such as Berg et al. tend to refer to inorganic phosphate, $\ce{P_i}$, as orthophosphate ($\ce{PO4^{3-}}$), the term inorganic phosphate is used because in aqueous solution at pH 7.6 several phosphate species exist, the predominant one being $\ce{HPO4^{2-}}$. If this is regarded as $\ce{P_i}$, then it is the source of the $\ce{H^{+}}$, and the equation balances.