ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

186 BRAHMAGUPTA AND ARITHMETIC have been quoted by his commentator Pṛthūdaka Svāmī in connection with one of his karaṇa-sūtra.¹

1. A horse was purchased by (nine) dealers in partner- ship, whose contributions were one, etc. up to nine; and was sold by them for five less than five hundred. Tell me what was each man's share of the sale proceed²
2. Four colleges (mathas), containing an equal num- ber of pupils, were invited to partake of a sacrificial feast. A fifth, a half, a third and a quarter (of the total number of pupils in the college) came from the respective colleges to the feast; and added to one, two, three and four, they were found to amount to eighty- seven; or, with those deducted, they were sixty seven. Find the actual number of the pupils that came from each college.³
3. Three (unequal) jars of liquid butter, of water and of honey, contained thirty-two, sixty and twenty-four Pala respectively; the whole was mixed together and the jars filled again. Tell me the quantity of butter, of water and of honey in each jar⁴.
4. प्रक्षेपयोगहृत्या लब्ध्वा प्रक्षेपका गुणा लाभाः । ऊनाधिकोत्तरस्तुतोनया स्वफलमूनयुत ॥ BrSpSi. XII. 16.
5. एकाद्यैर्नव पर्यन्तैर्वणिग्भिर्मूलराशिभिः । क्रीतो हयोऽसौ विक्रीतः पञ्चोनैः पञ्चभिः शतैः । किमैकैकस्य तत्रासीद् ब्रूहि त्वं मिश्रकान् मम ॥
6. मठस्थानानि चत्वारि छात्राणां समसंख्यया । भोक्तुं संमन्त्रितान्यासन् दीक्षायां किल यज्वना ॥ पञ्चार्धत्रिचतुर्थांशास्तेभ्यो भोक्तुं समागताः । एकद्वित्रिचतुर्युक्ता दृष्टाशीतिः ससप्तका ॥ एवोत्तरैरथवा हीना सप्तषष्टिश्चतैऽशकाः । मठेभ्यश्छात्रसंख्यां मे ब्रूहि ये चागता यतः
7. घृतोदक मधूनां ये त्रयः कलसकाः पलैः । रदषष्टिजिनैः पूर्णा एकीभूतास्ततः पुनः ॥ मिश्रेण पूरिता यावत् तावत् संख्यां न वेद्म्यहम् । घृतोदकमधूनां तामेकैकत्र गतां वद ॥ —: ० :—