Vateshvarasiddhanta 3.480_43

3.480_43

citra do dekhiye. na vṛttakendra. matra iṣṭacāpa, casa iṣṭacāpa koṭi,
cara - iṣṭacāpajyā mujāgrasaṃśaka. capa iṣṭracāpakoṭijyā dvitīya bhujāgrasaṃśaka
rama - iṣṭacāpa kī utkramajyā sujāyabhāgotkramajyā .
sapa = iṣṭacāpa koṭi kī utkramajyā dvitīya bhujāya bhāga kī utkramajyā .
nama = trijyā . nasa trijyā namarama tribhujāgrabhāgotkama jyā rana capa
dvitīya bhujāyasaṃjñaka koṭijyā
tathā nasa-sapanapa tridvitīyanujāgrabhāgotkramajyā tri- koṭyutkramajyā -
mujāyasaṃjñaka ghara bhujaṇyā .. 51-52 ..
idānīṃ bhujajyākoṭijyayorekato dvitīyajñānaṃ kramajyājñānaṃ cāha .
trijyā bāhvapramauyoṃḥ kṛtivivarapadaṃ vetarajyā praviṣṭā .
bāhvarājyā trirmodhyoṃvivarayutihatemū lamāhustayorvā .
vyāsasya vyastajīvā virahitanihateryatpadaṃ sā kramajyā .
vyāsaṣnā vyastajīvā nijakṛtirahitā mūlamasyāḥ kramajyā .. 53 ..
vi. mā. - trijyāvā hvagramauvyoṃḥ kṛtivivarapadaṃ (trijyābhujāgrajyayorva-
rgāntaramūlaṃ) itarajyā pradiṣṭādvitīyabhujāgrajyā kathitā) arthāt trijyābhujajyayo-
baṃgāntaramūle koṭijyā vā trijyākoṭijyayorvargāntaramūlaṃ bhujajyā bhavet. vā
tayorbāhvayajyā trimauvyoṃvivarayuttihaleḥ pada (trijyā mujārājyayoryogāntara-
dhātamūla) itarajyā (dvitīyabhujāgrajyo) āhuḥ (ācāryāḥ kathitavantaḥ) . vyasta-
jīvā birahitanihitaḥ (utkramajyā rahitaguṇitasya) vyāsasya pada (mūla) yat sā
kamajyā bhavati . vyastajīvā (utkramajyā) vyāsannā (vyāsaguṇitā) nijakṛti-
rahitā (svavargahonā) asyā mūlaṃ tadā kramajyā bhavatīti .. 53 ..

See Figure 2. na is the center of the circle. maca is the desired arc; casa is the complement of the desired arc. cara is the sine of the desired arc, designated as the base; capa is the cosine of the desired arc, designated as the second base. rama is the versed sine of the desired arc, the versed sine of the base degrees. sapa is the versed sine of the complement of the desired arc, the versed sine of the second base degrees. nama is the radius; nasa is the radius. nama - rama = radius minus the versed sine of the base degrees = rana = capa = the cosine designated as the second base. Likewise nasa - sapa = napa = radius minus the versed sine of the second base degrees = radius minus the versed sine of the complement = cara = the base-sine designated as the base. || 51–52
Now he states the determination of the second from one of the base-sine and cosine, and the determination of the sine:
The square root of the difference of the squares of the radius and base-sine is declared to be the other sine; / or they say it is the root of the product of the sum and difference of the base-sine and the radius. / That root of the diameter diminished and multiplied by the versed sine is the sine; / or the versed sine multiplied by the diameter, diminished by its own square—its root is the sine. || 53
Sanskrit commentary: The square root of the difference of the squares of the radius and the base-sine (the square root of the difference between the squares of the radius and the base-sine) is declared to be the other sine (stated as the second base-sine); that is, the square root of the difference between the squares of the radius and the base-sine is the cosine, or the square root of the difference between the squares of the radius and the cosine is the base-sine. Or, the root of the product of the sum and difference of the two, the base-sine and the radius (the root of the product of the sum and difference of the radius and the base-sine), the teachers say is the other sine (the second base-sine). The root of the diameter multiplied by [the diameter] diminished by the versed sine (multiplied after subtracting the versed sine) is the sine. The versed sine multiplied by the diameter (multiplied by the diameter) and diminished by its own square (minus its own square)—its root is then the sine. || 53