The Vedanta Sutras of Badarayana, Commentary by Sankara (SBE38), tr. by George Thibaut [1896] at sacred-texts.com
5. (The prânas are) seven, on account of this being understood (from scriptural passages) and of the specification (of those seven).
So far we have shown that there is in reality no conflict of scriptural passages regarding the origin of the prânas. It will now be shown that there is also no conflict regarding their number. The chief vital air (mukhya prâna) will be discussed later on. For the present the Sûtrakâra the number of the other prânas. A doubt arises here owing to the conflicting nature of the scriptural passages. In one place seven prânas are mentioned, 'The seven prânas spring from him' (Mu. Up. II, 1, 8). In another place eight prânas are mentioned as being grahas, 'Eight grahas there are and eight atigrahas' (Bri. Up. III, 2, 1). In another place nine, 'Seven are the prânas of the head, two the lower ones' (Taitt. Samh. V, 3, 2, 5). Sometimes ten, 'Nine prânas indeed are in men, the navel is the tenth' (Taitt. Samh. V, 3, 2, 3). Sometimes eleven, 'Ten are these prânas in man, and Âtman is the eleventh' (Bri. Up. III, 9, 4). Sometimes twelve, 'All touches have their centre in the skin,' &c. (Bri. Up. II, 4, 11). Sometimes thirteen, 'The eye and what can be seen,' &c. (Pr. Up. IV, 8).--Thus the scriptural passages disagree about the number of the prânas.
Here the pûrvapakshintains that the prânas are in reality seven in number, on account of understanding, i.e. because they are understood to be so many, from passages such as 'The seven prânas spring from him,' &c. These seven prânas are moreover specified in the other passage quoted above, 'Seven indeed are the prânas of the head.'--But in the same passage we meet with the following reiteration, 'Resting in the cave they are placed there seven and seven,' which intimates that there are prânas in addition to the seven.--No matter, we reply; that reiteration is made with reference to the plurality of men, and means that each man has seven prânas; it does not mean that there are two sets of seven prânas each of different nature.--But, another objection will be raised, other scriptural passages speak of the prânas as eight in number; how then should they be seven?--True, we reply, the number of eight also is stated; but on account of the contradictory nature of the statements we have to decide in favour of either of the two numbers; hence we decide in favour of the number seven, in deference to the (simpler) assumption of a low number, and consider the statements of other numbers to refer to the difference of modifications (of the fundamental seven prânas).--To this argumentation the next Sûtra replies: