The Universal System of Astronomy, Part Two

White etc.
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...from that point forward, in the first quadrant pūrvapada; the first 90-degree section of a circle, the calculation of the degrees follows the natural order. In the second quadrant dvitīyapada, the degrees are calculated in the order of the standard sine kramajyā starting from the radius trijyā; the total sine of 90 degrees.

Then, in the third quadrant tṛtīyapada, the calculation proceeds from the tip of the sky-line. In the fourth quadrant caturthapada, the position of the degrees is determined by the sequence of the horizon kṣitija, where the sky-line is diminished and meets the horizon. In these quadrants, the nodes original: pāta; the points where the planetary orbit intersects the ecliptic are calculated.

The sine-arm bhujā; the side of a right-angled triangle representing the sine subtracted from three signs original: tribha; three zodiac signs equal 90 degrees is called the base koṭi; the vertical side or cosine. This is used to determine the degrees of latitude at the equator vyakṣāṃśa; literally 'degrees of no-latitude'. By using the versed sine utkramajyā and the alignment of these positions, the movement is calculated.

The line drawn from the earth-line bhū-rekhā toward the circular boundary represents the path. The circumference of this circle is the boundary. Here, the versed sines utkramajyā are subtracted from the standard sines kramajyā. To demonstrate the calculation based on sixty Referring to the sexagesimal system where a circle is divided into 60 parts (ghatika) or the radius is often measured in units of 60, where the sines are placed in their respective parts: the standard sine kramajyā takes the form of a portion of the earth-line bhū-rekhā.

Outside of this, a portion of the earth-line is seen as the horizon kṣitija. From the middle of that single section, the calculation of the versed sines utkramajyā is completed. In the same way, by using the meridian line madhyasūtra, the positions are established on the rim of the circle. The base koṭi is sixty; the sine jyā acts as the hypotenuse karṇa, which is then transformed into the radius-hypotenuse trijyā-karṇa.

All of this is calculated to avoid error. Through the power of this base calculation, this friend The author uses 'mitra' (friend), which could be a poetic reference to the Sun or a mnemonic for a specific mathematical factor is proven. From the center of the quadrant...