आम्-प्रत्ययवत् कृञो ऽनुप्रयोगस्य

This sutra applies where the fruit of the action does not accrue to the agent. There are in Sanskrit two forms of the perfect tense (लिट्): one formed in the ordinary way by the reduplication of the root and adding the terminations; the other called the periphrastic perfect, is formed by adding आम् to the root, and then affixing to it the perfect tense of the roots कृ (to do), भू (to be ) or अस् ( to be ). These latter verbs are called anuprayoga or auxiliary verbs, as it is with their help that the perfect tense is formed. The question then arises, what conjugation, parasmai or atmanepada, do these auxiliaries take in forming the periphrastic perfect? This sutra supplies the answer :--the auxiliary कृ follows the conjugation of principals, the other auxiliaries do not. Thus the root एध (to increase, prosper) is atmanepadi, therefore in forming the periphrastic perfect, the verb कृ will be also in the atmanepada. Thus एधांचक्रे (he prospered). Similarly इद् (to appear with great splendour) is parasmaipadi and the auxiliary कृ after it will be parasmaipada, as इन्दाञ्चकार (he appeared with great splendour).
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But the other auxiliaries भू and अस् retain their own peculiar conjugation and are not influenced by the conjugation of their principal. Thus एधाम्बभूव, एधामास.

The word am-pratyaya of the sutra means 'that after which the affix am (III. I. 35) and (III. I. 36.) (कास्प्रत्ययादाममन्त्रे लिटि) comes.' Of the verb krin, when subjoined to another as an auxiliary, the termination is that of the atmanepada like the verb that takes the affix am. If this sutra enjoined a rule of injunction (vidhi), then there would be the termination of the atmanepada even in examples like उदब्जांचकार and उदम्भांचकार where the fruit of the action accrues to the agent. This is no valid objection to the present sutra. It is to be interpreted in both ways, that is, both as a vidhi (a general injunction) and a niyama (a restrictive injunction). How is that to be done? Because the word purvavat of the last sutra is to be read in the present aphorism also. The second explanation in that case will be for the sake of establishing a niyama or restrictive rule.

It has already been said above that the auxiliary verbs कृ, भू and अस् are used in forming the periphrastic perfect. This is done by force of the aphorism (III. I. 40), कृञ्चानुप्रयुज्यते लिटि, meaning, the verb krin is annexed in the perfect tense, to verbs, that take am. In this sutra (III. I. 40) the word krin is a pratyahara, implying the verbs कृङ्, भू and अस्. It might be asked how is this pratyahara formed? The word kri is taken from the fourth word of sutra 5.4.50, अभूतद्भावे कृभ्वस्तियोगे &c., and the letter n is taken from sutra 5.4.58 कृञोद्वितीय &c. This is the way in which the commentators explain how not only the verb krin is used as an auxiliary in forming the periphrastic perfect, but also the verbs भू and अस्. These three verbs denoting absolute action unmodified by any especial condition have in all languages been fixed upon as the best auxiliaries.

It must, however, be noted that the word krin in this sutra is not used as a pratyahara and consequently does not include the verbs भू and अस्.,