![Apastamba Sulba-sutra [sanskrit] - book cover](/uploads/a/Sulba-Sutra-Geometry.jpg)
Apastamba Sulba-sutra [sanskrit]
29,967 words
The Sanskrit edition of the Apastamba Sulba-sutra with the commentaries of Kapardin, Karavinda and Sundararaja. The Sulbasutras are considered Vedic appendices and deals with the ancient Indian science of Mathematics and Geometry, by instructing the construction of fire-altars, among others. Original titles: Āpastambaśulbasūtra (आपस्तम्बशुल्बसूत्र), Kapardin (कपर्दिन्), Karavinda (करविन्द), Sundararāja (सुन्दरराज)
Sutra 2.4b
hrasīyasaḥ karaṇyā varṣīyaso vṛddhram ullikhet | vṛddhrasyākṣṇayārajjur ubhe samasyati | tad uktam || Sūtra _2.4b ||
hrasīyasaḥ alpīyasaḥ kṣetrasya karaṇyā pramāṇena varṣīyasaḥ varṣīyasetyarthaḥ /
vṛddhraṃ dīrghamullikhet / yathālpīyasaḥ karaṇī tiryaṅbhānī varṣīyasaḥ karaṇī pārśvamānī, tathā dīrghacaturaśramullikhet / vṛddhrasyākṣṇayārajjurubhe samasyati / uktaṃ--dīrghacaturaśrasyākṣṇayārajjuriti /
tulyayoriti / samāso nāma samasanaṃ miśraṇaṃ ekīkaraṇaṃ karaṇītulyapramāṇayoḥsamāsaḥ / karaṇyuktā caturaśrasyākṣṇayārajjurddvistāvatīṃ bhūmiṃ karoti samasyeti / uktamanubhāṣaṇaṃ vakṣyamāṇārthaṃ, idamatra pariśiṣyate, tādidaṃ vakṣyāmīti /
nānāpramāṇayorbhinnapramāṇayoḥsamāsaḥ karaṇyucyate, hrasīyasaḥ alpīyasaścaturaścasya karaṇyā--karaṇīpramāṇena, barṣīyasaḥmahataścaturaśrasya, vṛddhraṃ--cihnamekadeśamullikhet vṛddhrasyākṣṇayārajjurubhe nānāpramāṇe caturaśre samasyati ekīkaroti / etaduktaṃ bhavati--nānārapramāṇe caturaśre samasya alpīyasaścaturaśrasya karaṇīpramāṇena mahadaścaturaśrasya ekasyāṃ tiryaṅbhānyāṃ paricchindyāt / tata ārabhyordhvāṃ lekhāṃ yathā parasyāṃ tiryaṅbhānyāṃ tāvati pradeśe nipatati tathā likhet / lekhāvibhaktasyālpīyasaḥ karaṇīpramāṇaṃ tiryaṅbhānī / kasya? mahataḥ karaṇīpramāṇapārśvamānīkasya dīrghacaturaśrasyākṣṇayārajjurume nānāpramāṇe caturaśre samasyati / caturaśra iti vartamāne punaścaturaśragrahaṇaṃ maṇḍalayorapi caturaśraṃ kṛtvaiva samāsaḥsukara iti jñāpayituṃ / taduktaṃ--dīrghasyetyādinā / asyopayogo vidyābhyāsādiṣu /
dvikaraṇyā yathā dvipuruṣe'gnau puruṣadvikaraṇyā dvayoḥ puruṣayoḥsamāsa ityādi / trikaraṇyā trayāṇāṃ puruṣāṇāṃ samāsasyāpyetadupalakṣaṇaṃ bhavati /
dīrghacaturaśrayostu samāse ayaṃ viśeṣaḥ / tiryaṅbhānyā dvikaraṇī tiryaṅbhānī, pārśvamānyāś ca dvikaraṇī pārśvamānīti / yathā dvistāvāyāmāśvamedhavedyāṃ ṣaṭtriṃśikāyāḥ pṛṣṭhyāyā dvikaraṇī pṛṣṭhyā / tiryaṅbhānyostriṃśikārāntareṇa vakṣyate / prakramasya dvikaraṇī prakamasthānīyā bhavatīti / evaṃ dīrghacaturaśrāṇāṃ samāse tiryaṅmānyāstrikaraṇī tiryaṅmānīti / pārśvamānyāś ca pārśvamānī / yathā--tristāve'gnau pakṣayoḥ puruṣamātrayāḥ tiryaṅmānyāstrikaraṇī aṣṭādhikaśatadvayāṅgulā pañcatilonā tiryaṅmānī bhavati / pārśvamānyāś ca ṣaḍaratneḥ trikaraṇī pañcāśahdviśatāṅgulā viṃśatitilonā pārśvamānī bhavati / pucchasya pārśvamānyā ekādaśaprādeśāyāḥ trikaraṇī aṣṭāviṃśatidviśatāṅgulā pārśvamānī / evamanyatra /
hrasīyasaḥ karaṇīṃ tiryaṅmānīṃ kṛtvā varṣīyasaḥsaṃbandhinaṃ vṛrdhaṃ dīrghacaturaśramullikhet, varṣīyasaḥ karaṇyeva pārśvamānī / evaṃ kṛtasya dīrghacaturaśrasyākṣṇayārajjuḥsamastuyoḥ karaṇī bhavati / taduktaṃ "dīrghasyākṣṇayārajjuḥ' ityādinā / yathā pañcavidhe'gnau kliyamāṇe dvipuruṣeṇa caturaśre kṛte catuṣpuruṣo bhavati / tatra puruṣamātraścaturaśraḥ prakṣeptavyaḥ / tatra dvipuruṣakaraṇike caturaśre tadāyāmaṃ puruṣavyāsaṃ dīrghacaturaśramullikhet / tasyākṣṇayārajjuraṣṭaṣaṣṭiśatāṅgulā saikādaśatilā, sā pañcavidhāgneḥ karaṇī bhavati /