द्विस्-त्रिश्-चतुर् इति कृत्वो ऽर्थे

The affix सुच् (स्) is added to the three words dvi, tri and chatur in the sense of krtvasuch by 5.4.18.

As द्विः करोति or द्विष्करोति, त्रिः करोति or त्रिष्करोति, चतुः करोति or चतुष्करोति, द्विः पचति or द्विष्पचति, त्रिः पचति or त्रिष्पचति, चतुः पचति or चतुष्पचति ॥

Why do we say 'when used in the sense of kritvasuch or Numeral adverbs '? Observe चतुष्कपालम्, चतुष्कण्टकम्, where ष is compulsory by 8.3.41. चतुर्षु कपालेषु संस्कृतः 4.2.16 and 4.1.88. This sutra is an example of ubhayatra-vibhasha. With regard to चतुर् the visarga is a non-affix visarga, and hence 8.3.41, would have made ष compulsory, this makes it optional. With regard to द्विस् and त्रिस् the visarga is that of an affix (सुच् or स् 5.4.18), and hence 8.3.41, would not have applied. Thus with regard to चतुर् it is a Prapta-vibhasha, and with regard to द्विस् and त्रिस् it is an Aprapta vibhasha.

Why have we used the words 'dvis, tris and chatur'? Objector's answer: so that the rule may not apply to पंचकृत्वः करोति, the visarga of kritvasuch 5.4.17 is not changed to ष् ॥

The anuvritti of उ and इ is understood here from 8.3.41: so that the visarga must be preceded by इ and उ for the application of this rule. In पञ्चकृत्वः the visarga is preceded by अ, and so there is no applicability of this rule.

In fact, by reading the anuvritti of इदुदुपधा into this sutra, and qualifying the visarga by the further epithet of 'belonging to a word that has the sense of kritvasuch'; we may dispense with the words द्विस्त्रिश्चतुरिति from the sutra. The simple sutra कृत्वोर्थे would have been enough. For there are no other Numerals that have a penultimate इ or उ, except these three. The chief objection to this view is, that in चतुर् the visarga is not the affix सुच्, but a portion of the word (See 5.4.18): so the rule would not apply to chatur, if this word were not expressly mentioned.

The various objections and their solutions are given in the following verses.

कृत्वसुजर्थे षत्वं ब्रवीति कस्माच्चचतुष्कपाले मा
षत्वं विभाषया भूम्ननु सिद्धं तत्र पूर्वेण ॥
सिद्धे ह्ययं विधत्ते चतुरः षत्वं यदापि कृत्वोर्थे ॥
लुप्ते कृत्वोर्थीये रेफस्य विसर्जनीयो हि ॥
एवं सति त्विदानीं द्वित्त्रिश्चतुरित्यनेन किं कार्यम् ॥
अन्यो हि नेदुदुपधः कृत्वोर्थः कश्चिदप्यस्ति ॥
अक्रियमाणे ग्रहणे विसर्जनीयस्तदा विशेष्येत ॥
चतुरो न सिध्यति तथा रेफस्य विसर्जनीयो हि ॥
तस्मिंस्तु क्रियमाणे युक्तं चतुरो विशेषणं भवति ॥
प्रकृतं पदं तदन्तं तस्यापि विशेषणं न्याय्यम् ॥

Karika:- कृत्वसुजर्थे षत्वं ब्रवीति कस्मात्? Why does the author teach षत्व when these words have the sense of Numeral-adverbs? In other words, why the word कृत्वोर्थे is used at all in the sutra? There is no necessity of using it at all, because द्विस्, त्रिस् are clearly adverbs as they are formed by the affix सुच् 5.4.18 and चतुर् being read in their company will also denote the adverb chatur, in which सुच् has been elided 5.4.18. So that all these three words are सुच्-formed, and all सुच्-formed words have the sense of Krtvasuch. One answer to this is that the rule of साहचर्य does not always hold good, as in दीधीवेवीटाम् 1.1.6, the words दीधी and वेवी are verbs, while इट् is an augment. Though therefore द्विस् and त्रिस् are krtvortha words, yet चतुर् need not be so: and may be a simple Numeral. Answer: चतुष्कपाले मा षत्वं विभाषया भूत् ॥ The word कृत्वोर्थे is employed to indicate that there should be no optional षत्व in चतुष्कपालं ॥ The षत्व here is compulsory by 8.3.41. Question: ननु सिद्धं तत्र पूर्वेण ॥ Well this would be valid by the previous sutra 8.3.41. That is, let in चतुष्कपाल also there be optional षत्व, as चतुःकपाल and चतुष्कपाल ॥ Now rule 8.3.41 will apply to चतुःकपाल and will change this visarga to ष, so that with regard to चतुष्कपाल, we shall have always ष ॥ Answer:- सिद्धे ह्ययं विधत्ते चतुरः षत्वं यदापि कृत्वोर्थे, लुप्ते कृत्वोर्थीये रेफस्य विसर्जनीयो हि । If 8.3.41 be considered as applying here (siddha), then when the affix सुच् is elided after चतुर्, and the र is changed to visarga, then the adverb चतुः also ends with a non-affix visarga, and will come under the compulsory षत्व rule of 8.3.41; for though we may have optionally two forms as चतुः करोति and चतुष्करोति, by the present sutra, yet in the former the visarga would be changed to ष by 8.3.41. Hence the necessity of employing the word कृत्वोर्थे ॥ Question: But we say that the र् in the adverb चतुर् is that of सुच्, thus चतुर् + स् = चतुर् + र् 8.2.66 = चतु + र् (the first र् is elided by 8.3.14) = चतुर्; and that this र् when changed to visarga, will be an affix-visarga and so 8.3.41 will not apply to the adverb चतुर् ॥ Answer:- No. For उ would require to be lengthened by 6.3.111. and the form would be चतूर् ॥

एवं सति त्विदानीं द्विस्त्रिश्चतुरित्यनेन किं कार्यम् ॥ If this be so, then what is the purpose served by using the words द्विस् त्रिश्चतुरिति in the aphorism? The simple sutra कृत्वोऽर्थे would have been enough. Because (अन्योहि नेदुदुपधः कुत्वोर्थः कश्चिदप्यस्ति) there are no other numeral adverbs than these three which have a penultimate इ or उ ॥

अक्रियमाणे ग्रहणे विसर्जनीयस्तदा विशेष्येत । If we do not use the words dvis, tris, chaturiti in the sutra, then the word krtvorthe would qualify the word visarga, and the sutra would mean \ the visarga of an affix which has the sense of kritvasuch is changed optionally to ष\ ॥ The result of this will be that (चतुरा न सिध्यति तथारेफस्य विसर्जनीयोहि) it will not apply to चतुः where the visarga is that of र् and not of the affix सुच् ॥

Therefore by using dvis &c, the word कृत्वोर्थे would qualify चतुर् (तस्मिन् तु क्रियमाणे युक्तं चतुरो विशेषणं भवति) ॥

Answer:- प्रकृतं पदं तदन्तं तस्यापि, विशेषणं नाय्यम् ॥ Though we may not use dvis &c, the word krtvortha will not qualify visarga, but will qualify the word पद whose context runs here; and the rule of तदन्त will apply; so that the sutra कृत्वोऽर्थे will mean, पदस्य कृत्वोर्थे वर्त्तमानस्य यो विसर्जनीयः, तस्य सकारः षकारो व ॥ \The visarga of that word which is employed in the sense of a Numeral adverb, is optionally changed to स् or ष् before a guttural or a labial, provided that such visarga is preceded by इ or उ\.

The above is the opinion of Patanjali, who considers the words dvis &c, as redundant. The Kasika however controverts this opinion. According to him, if these words were not used in the sutra, then the mere sutra कृत्वोऽर्थे would be insufficient for the visarga of चतुः though used as an adverb, the षत्व will be compulsory by 8.3.41; for the present sutra will be considered as asiddha or non-existent for the purposes of 8.3.41, (See 8.2.1). But this however may be answered by saying that the rule of पूर्वत्रासिद्धम् applies in these chapters, with this modification, one subject-matter is considered as asiddha with regard to another subject-matter gone before; but one aphorism is not considered asiddha with regard to a previous aphorism, when belonging to the same subject matter. (प्रकरणे प्रकरणमसिद्धं न योगे योगः) ॥ Therefore the present sutra 8.3.43, would not be considered asiddha with regard to 8.3.41. Or the present sutra may be considered as an apavada to 8.3.41: and an apavada is never asiddha with regard to an utsarga.,