Step 1: Understanding the Concept:
The history of Jyotiṣa is enriched by various scholars who contributed mathematical theories, astronomical observations, and predictive treatises. This question tests the knowledge of important classical and medieval texts and their authors.
Step 2: Detailed Explanation:
1. Siddhāntatattvavivēka (A): This is a major astronomical work by Kamalākarabhaṭṭa (III) (17th century). It is known for its detailed mathematical treatment and its critique of certain earlier Siddhantic constants based on fresh observations.
2. Trikōṇamiti (B): While Trigonometry is ancient in India (Jyā/Koti-jyā), specifically formalizing it as a distinct modern field in the late medieval/early modern context is associated with Bāpudēva Śāstrī (I). He was a 19th-century scholar from Varanasi who bridged traditional Siddhantic mathematics with Western mathematical developments.
3. Siddhāntadarpaṇa (C): This is the famous work of Sāmanta Candraśēkhara (IV) (1835-1904), also known as Pathani Samanta. He is renowned for achieving extreme observational accuracy using simple hand-made instruments (like the Mana-yantra) without using telescopes.
4. Laghuparāśarī (D): This is a concise predictive text based on the principles of Maharṣi Parāśara (II). It focuses on the functional benefics and malefics for different ascendants and the interpretation of Vimshottari Dasha. It is one of the most studied texts for 'Ududasha' interpretation.
Matching:
- A (Siddhāntatattvavivēka) \(\rightarrow\) III (Kamalākara)
- B (Trikōṇamiti) \(\rightarrow\) I (Bāpudēva)
- C (Siddhāntadarpaṇa) \(\rightarrow\) IV (Candraśēkhara)
- D (Laghuparāśarī) \(\rightarrow\) II (Parāśara)
These works represent different eras of Indian science, from the ancient Sūtras of Parāśara to the observational genius of Pathani Samanta in the 19th century.
Step 3: Final Answer:
The correct match is A-III, B-I, C-IV, D-II.