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

102 BRAHMAGUPTA'S KHAṆḌAKHĀDYAKA Now log [ 126 / 594 ] = 1.3265841. The values of the ∠PMK and the ∠PEM and Brahma- gupta's values as given in the verse¹ are presented below in a tabular form : | ∠PMK = | 28° | 60° | 90° | 121° | 135° | 148° | 164° | 173° | | ∠PEM = | 10°58′ | 23°1′ | 33°1′ | 39°56′ | 40°23′ | 37°31′ | 25°32′ | 12°35 | | Brahmagupta's ∠PEM = | 11° | 23° | 33° | 40° | 40°30′ | 37°30′ | 25°30′ | 12°30′ | It will be seen that Brahmagupta gives the values of the equation within 1/8th of a degree. It seems inexplicable why such discrepancies should remain in Brahmagupta's calculations. It is probable that he wanted to state his equations to the nearest half a degree. Now we shall take up the Śīghra equations of Mars, and then revert to the Sine Rule. We have in the Khaṇḍakhā- dyaka : Mars, by the degrees of Śīghra anomaly (i.e. anomaly of conjunction) of 28 getting at the corresponding equation of 11° rises (heliacally) in the east ; by the next 32° gets 12° more of the equation ; by the next 30°, 10° more ; by the next 31°, 7°, more ; by next 14°, half a degree ; these are positive ; by the next 13°, nega- tive 3° ; by the next 16° ; negative 12° after this he is retrograde ; by the next 9°, negative 13° ; by the next 7°, negative 12½°. After this the parts of the equations occur in the reverse order¹. On the basis of this we have the following table of the Śīghra equations for Mars : | Degrees of anomaly | Equation of | Phenomena | | of conjunction | conjunction | | | 0° | 0° | Motion direct. | | 28° | +11° | Rises in the east. |

1. भौमोऽष्ट्यग्नौ रुद्रान् भुक्त्वा पूर्व्वौदितोऽदरैर्कान् । ख_णैर्दशरूपगुणैः सप्तांशा मनुभिरर्द्धांशान् ॥ धनम् 'मग्नि शशाङ्कैस्त्रिनष्ट्या भास्करात्नतो वक्री । नवभिश्च योदशनगैर्द्वादशसार्द्धान् विलोमोऽतः ॥ KK.II.8-9