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सगोत्रेण अन्य गोत्रेण वा नियुक्तेन क्षेत्र जातः क्षेत्रजः पुत्रः ॥
the son begotten on a wife by another man, appointed for the purpose, and of the same gotra as that of the husband; or of a different gotra, is called kshetraja.
english translation
जनयितुर् असत्य् अन्यस्मिन् पुत्रे स एव द्वि पितृको द्वि गोत्रो वा द्वयोर् अपि स्वधा रिक्थ भाग् भवति ॥
on the death of the begetter, the kshetraja son will be the son to both the fathers, follow the gotras of both, offer funeral libations to both, and take possession of the immovable property (ríktha) of both of them;
english translation
तत् सधर्मा बन्धूनां गृहे गूढ जातस् तु गूढजः ॥
of the same status as the kshetraja is he who is secretly begotten in the house of relatives and is called gúdhaja, secretly born.
english translation
बन्धुना उत्सृष्टो अपविद्धः संस्कर्तुः पुत्रः ॥
the son cast off by his natural parents is called apaviddha and will belong to that man who performs necessary religious ceremonials to him.
english translation
कन्या गर्भः कानीनः ॥
the son born of a maiden (before wedlock) is called kánína.
english translation