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The lunar date (Tithi) occurring at that time should be accepted; this is the meaning. The rest is clear. For example: take the Shaka year 1514 1592 CE, subtract 1445 original: "arrows (5), ages (4), oceans (4), moon (1)" - a poetic way of writing 1445, which leaves 69. Multiply by 11 original: "Rudras" to get 759. The OCR text 781 appears to be a transcription error for 759 based on the math provided. Place this separately. Divide by 180 original: "void (0), mountains (7), earth (1)" - likely 170 or 180 depending on the system. The quotient is 4. Add this to the top number to get 763. Add 11 to this sum to get 774. Divide by 30 original: "void (0), fire (3)"; the remainder is 24. The quotient is not needed. This remainder is the Constant (Dhruva). By adding the specific additive for each solar transit (Sankranti), the lunar date is found. For example, the additive for the Aries transit is 0; the Constant 16 referring to the example remainder plus 0 is 16. Thus, the Aries transit is known to occur on the first day of the dark fortnight (Krishna Pratipat). Other dates should be calculated similarly. However, the "Day-Regulator" is the secret key here. || 17 ||
Regarding the nature of the signs, "dry" etc.—Aries is "of few offspring," meaning it results in limited progeny. || 18 ||
Regarding "Gemini" etc.—Gemini original: "Mithuna" has moderate offspring, meaning neither too few nor too many children. Cancer has many offspring, meaning it produces many progeny. || 19 ||
Sankranti: The moment the Sun enters a new zodiac sign.
Tithi: A lunar day, roughly 1/30th of a lunar month.
Dhruva: A mathematical constant used in astronomical calculations.
Shaka: An era of the Indian calendar starting in 78 CE.