BhG 18.13

syntax

he mahā-bāho (O mighty-armed one!),
[tvam] (you) etāni pañca kāraṇāni (these five causes) me (from me) nibodha (you must know).
sāṅkhye (in sāṁkhya) kṛtānte [ca] (and in the conclusion done) sarva-karmaṇām (of all activities) siddhaye (for perfection) [etāni] proktāni (which are declared) [santi] (they are).

grammar

pañca	–	pañca 2n.3 n. – five;
etāni	–	etat sn. 2n.3 n. – these;
mahābāho	–	mahā-bāhu 8n.1 m.; BV: yasya bāhū mahāntau staḥ saḥ – O mighty-armed one! (from: √mah – to magnify, mahant – great; √baṁh – to grow, to increase, bāhu – the arm);
kāraṇāni	–	kāraṇa 2n.3 n. – cause, motive, principle, the means (from: √kṛ – to do, karaṇa – deed, direct cause, instrument, helper);
nibodha	–	ni-√budh (to know) Imperat. P 2v.1 – you must know;
me	–	asmat sn. 6n.1 – my (shortened form of: mama);
sāṁkhye	–	sāṁkhya 7n.1 n. – in sāṁkhya (from: sam-√khyā – to count, sāmkhya – relating to number, rational, one of the schools of Hindu philosophy);
kṛtānte	–	kṛta-anta 7n.1 n.; BV: yasyāntaḥ kṛto ‘sti tasmin – in that which has the conclusion, in Vedānta (from: √kṛ – to do, kṛta PP – done, made; anta – the end, limit, boundary);
proktāni	–	prokta (pra-√vac – to declare, to speak) PP 1n.3 n. – which are declared, which are spoken;
siddhaye	–	siddhi 4n.1 f. – for accomplishment, for fulfilment, for perfection, for success (from: √sidh – to succeed, to become perfect);
sarva-karmaṇām	–	sarva-karman 6n.3 n.; TP: sarveṣāṁ karmaṇām iti – of all activities (from: sarva – all, whole; √kṛ – to do, karman – activity and its result);

textual variants

pañcaitāni → pañcemāni (these five);
mahābāho → mahābhāga (O fortunate one!);

Śāṃkara

ataḥ paramārtha-darśina evāśeṣa-karma-saṃnyāsitvaṃ sambhavaty avidyādhyāropitatvād ātmani kriyā-kāraka-phalānām | na tv ajñasyādhiṣṭhānādīni kriyā-kartṛ-kārakāṇy ātmatvenaiva paśyato’śeṣa-karma-saṃnyāsaḥ sambhavati | tad etad uttaraiḥ ślokair darśayati—
pañcaitāni vakṣyamāṇāni | he mahābāho ! kāraṇāni nirvartakāni | nibodha me mameti uttaratra cetaḥ-samādhānārtham, vastu-vaiṣamya-pradarśanārthaṃ ca | tāni ca kāraṇāni jñātavyatayā stauti—sāṅkhye jñātavyāḥ padārthāḥ saṃkhyāyante yasmin śāstre tat sāṃkhyaṃ vedāntaḥ | kṛtānte iti tasyaiva viśeṣaṇam | kṛtam iti karmocyate, tasyāntaḥ parisamāptir yatra sa kṛtāntaḥ, karmānta ity etat | yāvān artha udapāne [gītā 2.46] sarvaṃ karmākhilaṃ pārtha jñāne parisamāpyate [gītā 4.33] ity ātma-jñāne saṃjāte sarva-karmaṇāṃ nivṛttiṃ darśayati | atas tasmin ātma-jñānārthe sāṃkhye kṛtānte vedānte proktāni kathitāni siddhaye niṣpatty-arthaṃ sarva-karmaṇām

Rāmānuja

idānīṃ bhagavati puruṣottame antaryāmiṇi kartṛtvānusaṃdhānena ātmani akartṛtvānusaṃdhānaprakāram āha, tata eva phalakarmaṇor api mamatāparityāgo bhavatīti / paramapuruṣo hi svakīyena jīvātmanā svakīyaiś ca karaṇakalevaraprāṇaiḥ svalīlāprayojanāya karmāṇy ārabhate / ato jīvātmagataṃ kṣunnivṛttyādikam api phalam, tatsādhanabhūtaṃ ca karma paramapuruṣasyaiva /
sāṃkhyā buddhiḥ, sāṃkhye kṛtānte yathāvasthitatattvaviṣayayā vaidikyā buddhyā anusaṃhite nirṇaye sarvakarmaṇāṃ siddhaye utpattaye, proktāni pañcaitāni kāraṇāni nibodhe me mama sakāśād anusaṃdhatsva / vaidikī hi buddhiḥ śarīrendriyaprāṇajīvātmopakaraṇaṃ paramātmānam eva kartāram avadhārayati, „ya ātmani tiṣṭhan ātmano ‚ntaro yam ātmā na veda yasyātmā śarīraṃ ya ātmānam antaro yamayati sa ta ātmāntaryāmy amṛtaḥ”, „antaḥpraviṣṭaḥ śāstā janānāṃ sarvātmā” ityādiṣu

Śrīdhara

nanu karma kurvataḥ karma-phalaṃ kathaṃ na bhaved ity āśaṅkya saṅga-tyāgino nirahaṅkārasya sataḥ karma-phalena lepo nāstīty upapādayitum āha pañceti pañcabhiḥ | sarva-karmaṇāṃ siddhaye niṣpattaya imāni vakṣyamāṇāni pañca-kāraṇāni me vacanān nibodha jānīhi | ātmanaḥ kartṛtvābhimāna-nivṛtty-artham avaśyam etāni jñātavyānīty evam | teṣāṃ stuty-artham evāha sāṅkhya iti | samyak khyāyate jñāyate paramātmā ‚neneti sāṅkhyaṃ tattva-jñānam | prakāśamāna ātma-bodhaḥ sāṅkhyam | tasmin kṛtaṃ karma tasyāntaḥ samāptir asminn iti sāṅkhyam | kṛto ‚nto nirṇaye ‚sminn iti kṛtāntaṃ sāṅkhya-śāstram eva | tasmin proktāni | ataḥ samyaṅ nibodha ity arthaḥ |

Viśvanātha

nanu karmakurvataḥ karma-phalaṃ kathaṃ na bhaved ity āśaṅkya nirahaṅkāratve sati karma-lepo nāstīty upapādayitum āha pañcamānīti pañcabhiḥ | sarva-karmaṇāṃ siddhaye niṣpattaya imāni pañca-kāraṇāni me mama vacanān nibodha jānīhi | samyak paramātmānaṃ khyāti kathayati iti saṅkhyam eva sāṅkhyaṃ vedānta-śāstraṃ tasmin | kīdṛśe kṛtaṃ karma tasyānto nāśo yasmāt tasmin proktāni |

Baladeva

nanu karmāṇi kurvatāṃ tat-phalāni kuto na syur iti cet svasmin kartṛtvābhiniveśa-tyāgena parameśvare mukha-kartṛtva-niścayena bhavatīty āśayenāha pañcaitānīti pañcabhiḥ | he mahābāho sarva-karmaṇāṃ siddhaye niṣpattaye etāni pañca-kāraṇāni me matto nibodha jānīhi | pramāṇam āha sāṅkhya iti | sāṅkhyaṃ jñānaṃ tat-pratipādakaṃ vedānta-śāstram sāṅkhyaṃ tasmin | kīdṛśīty āha kṛtānte kṛta-nirṇaye sarveṣāṃ karma-hetūnāṃ pravartakaḥ paramātmeti nirṇaya-kāriṇīty arthaḥ | antaryāmi-brahmaṇe viditam etat | ihāpi sarvasya cāhaṃ hṛdi (Gītā 15.15) ity ādy uktaṃ | vakṣyate ca īśvaraḥ sarva-bhūtānām (Gītā 18.61) ity ādi |