The Vedanta Sutras of Badarayana, Commentary by Sankara (SBE38), tr. by George Thibaut  at sacred-texts.com
43. (The soul is) a part of the Lord, on account of the declarations of difference, and (because) in a different way also some record that (Brahman) is of the nature of slaves, fishers, and so on.
We have shown that the individual soul and the Lord stand to each other in the relation of what is being acted upon and what is acting upon. This relation is observed in ordinary life to exist only between things connected, such as a master and a servant, or a fire and its sparks. Now as the soul and the Lord also are acknowledged to stand in the relation of what is acted upon and what is acting, a doubt arises whether their connexion is analogous to that of a master and a servant, or to that of a fire and its sparks.
The pûrvapakshin maintains that either the matter is to be considered as undetermined, or that the connexion is like that of master and servant, because that connexion only is well known to be the relation of ruler (Lord) and subject ruled.
To this the Sûtra replies that the soul must be considered a part of the Lord, just as a spark is a part of the fire. By 'part' we mean 'a part as it were,' since a being not composed of parts cannot have parts in the literal sense.--Why, then, do we not view the Lord, who is not composed of parts, as identical with the soul?--'On account of the declarations of difference.' For such scriptural passages as 'That (self) it is which we must search out, that it is which we must try to understand' (Kh. Up. VIII, 7);
[paragraph continues] 'He who knows him becomes a muni' (Bri. Up. IV, 4, 22); 'He who dwelling within the Self pulls the Self within' (Bri. Up. III, 7, 23); which all of them refer to a difference (between the highest and the individual Self) would be inappropriate, if there were no difference.--But, it may be said, these statements of difference would agree better with a relation similar to that of master and servant.--Hence the sûtrakâra adds, 'and otherwise also.' That the soul is a part (of the Lord) we learn not only from the passages declaring their difference, but there are other statements also which teach their non-difference. The members of a certain sâkhâ of the Atharva-veda record in a Brahma-sûkta that 'Brahman are the fishermen, Brahman the slaves, Brahman these gamblers,' &c. Here low creatures such as fishermen, and slaves depending on their masters, and gamblers are called Brahman; whence it appears that all individual souls which have entered into aggregates of effects and instruments (i.e. bodies) depending on name and form are Brahman. The same view is set forth in other passages such as 'Thou art woman, thou art man; thou art youth, thou art maiden; thou as an old man totterest along on thy staff, thou art born with thy face turned everywhere' (Sve. Up. IV, 3), and 'The wise one who, having produced all forms and made all names, sits calling (the things by their names)' (Taitt. Âr. III, 12, 7). Passages such as 'There is no other seer but he' and other similar ones establish the same truth.--Non-differenced intelligence belongs to the soul and the Lord alike, as heat belongs to the sparks as well as the fire.--From these two views of difference and non-difference there results the comprehensive view of the soul being a part of the Lord.--The following Sûtra supplies a further reason.