Discernment of the Truth of Astronomical Principles

The Mathematical Ratio of the Sphere

The diameter Vyāsa|The straight line passing through the center of the Earth-sphere and the circumference Paridhi|The total distance around the Earth's surface are related in a fixed proportion. In the works of Bhaskara original: bhāskarīyaiḥ; referring to Bhaskaracharya, the 12th-century Indian mathematician and astronomer, these measurements are calculated and inscribed using a specific formula. By examining his methods, we find the remainder of the calculation. 14

Through a division using the factor of eight, twenty-four, five, and thirty-two original: 8। 24। 5। 32; these likely refer to specific fractional parts or sexagesimal units used in ancient trigonometry, the method taught by Bhaskara is correctly applied to determine the circle's diameter. From this, the true nature of the circular root is known. 15 Some observers see a width of 28,308 a value related to the Earth's measure, which is fixed and consistent with the views of the Solar School Saura|The tradition or astronomical school following the Surya Siddhanta. 16 To ensure the understanding of his students and to resolve disputes, this calculation is performed for the sake of clear solar realization. 17

Methods of Calculation

Square the diameter and multiply it by ten; then, the square root of that result provides the circumference. Conversely, the diameter can be found by reversing this process. 18 Alternatively, square the circumference, then divide that square by ten; the square root of the result will give the diameter through the reverse operation. 19 Whenever the square root must be extracted, one should follow the prescribed method of calculation. 20

The circumference is described as being the square root of ten original: dashamūla; a common ancient approximation for Pi (π) where π ≈ √10, or roughly 3.162. 21 When the desired diameter is multiplied by this value, the result is produced. In some calculations, the square is 53,293. 22 Thus, the square of one's own diameter results in the circumference in many ways. However, it must be noted that in some traditions, the diameter and circumference are not considered perfectly fixed. 23

The Dimensions in Yojanas

In the measurement of hundreds of Yojanas Yojana|A traditional unit of distance, roughly 5 to 9 miles depending on the text, the Earth’s measure is given as 39,600. 25 According to the Solar and Manu traditions, there are variations in these counts because of different standards of measurement. This difference in numbers is explained by their own teachers. In the calculations of the Romakas original: romaka; referring to the Greco-Roman or Alexandrian astronomical tradition, the math follows a different method. 26 That which follows the measurement of the inhabited world is used for the measure of the Earth; those who speak otherwise do so out of ignorance of the mathematical methods. 27

The Meridians and Local Positions

The North-South line Yāmyottara-rekhā|The prime meridian or local longitude line passes through one’s own location and connects to Meru the North Pole. 30 Just as Meru is the starting point, the locations of other cities are determined by these lines. 31 Where a line is drawn according to its own degrees of latitude, those degrees define that city's position and no other. 32 From the circumference of one’s own side to the desired location in yojanas, the distance is calculated from the middle. 33

To the South of Meru, the city of Lanka is situated at a distance of 22 degrees original: bhāgaiḥ; degrees; it is well-known that the line passes through there. 34 The line connecting the rising point of Meru and one's own country is established with great effort. 35