Siddhanta Shiromani (Crown of Treatises)

How is the calculation of four hundred thousand increased by thirty-two thousand original: dvātriṃśat-sahasrādhika-caturbhir-lakṣaiḥ; referring to the base number 432,000 determined? It is expressed through the symbolic words: "sky, cloud, cloud, teeth, and oceans" This uses Bhūta-saṅkhyā, a system where words represent numbers: sky/void (kha) = 0, cloud (abhra) = 0, teeth (danta) = 32, and oceans (sāgara) = 4. Read together, they represent 432,000.. In sequence, these are multiplied by four, three, two, and one respectively to determine the duration of the ages, beginning with the Krita Age. Therefore, using the base of 432,000:

By multiplying by four, the result is 1,728,000; this is the first "foot" or quarter of the Great Age, known as Krita kṛta-yuga.

By multiplying by three, the result is 1,296,000; this is the second quarter of the age, named Treta tretā-yuga.

By multiplying by two, the result is 864,000; this is the third "foot" of the age, called Dvapara dvāpara-yuga.

By multiplying by one, the result is 432,000; this is the fourth quarter of the age, named Kali kali-yuga.

What is the nature of these "feet" of the ages? They are accompanied by a dawn sandhyā and a twilight sandhyāṃśa. They are constituted in such a way that they include portions measured as one-twelfth of their own total length. Regarding these quarters, some authorities state that these specific parts are included within the total.

In this context, the "dawn" of a particular quarter is equal to one-twelfth of that quarter's total duration; it occurs at the beginning of the period. An identical amount occurs at the end of the period as the "twilight." This is the meaning when it is said that the quarters are described as being joined with their transitional periods.

In this explanation, the word "their" original: tat in the phrase "their parts" acts as a general indicator for each individual quarter. To provide an example, let us look at the measurement of the Krita Age: 1,728,000.

One-twelfth of this is 144,000. This amount constitutes the dawn at the beginning of the Krita Age, and exactly the same amount, 144,000, constitutes the twilight at the end. In the middle, the main body of the Krita Age measures 1,440,000. When these are all added together, the total is 1,728,000, which is the full "foot" of the age named Krita.