पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

114 PAÑCASIDDHĀNTIKĀ IV. 40 The arc of 84' 30" is 44° 46'. Therefore the Sun rises at a point 44° 46' north of the east point, and sets at a point 44° 46" north of the west point, (assuming that the declination has not changed). The formula for amplitude is got thus: See Fig. 12. Take S₁ as the Sun on the diurnal circle north of equator. Then S₁S₂ is the declination of the Sun, D₁D₂ is the amplitude of sunrise. From the figure it can be seen, D₁D₂ = 90° − ND₁ Therefore sin D₁D₂ = Cos ND₁. From the right angled triangle ND NP in the figure, Cos ND can be got thus: By the fundamental formula I, Cos ND₁ = 120' × Cos D₁ NP ÷ Cos N NP. But, Cos D₁ NP = Cos S₁ NP = Cos (90° − S₁S₂) = sin S₁S₂ = sin S₁S₂ Cos N NP = sin (90° − N NP) = sin colat. ∴ Sin amplitude = 120' × sin dec ÷ sin colat. When the Sun is south of the celestial equator, (e.g. S₃ in the figure), D₃ is the rising point, and D₂D₃ is the amplitude. Its sine is got thus, from the triangle, D₂D₃E, right-angled at E. By the funda- mental formula II, Sin D₂D₃ = sin ED₃ × radius ÷ sin angle D₃D₂E, Here, ED₃ is the declination. D₃D₂E = 90° − ED₂Z = 90° − lat. ∴ sin amplitude = sin declination × radius ÷ sin (90° − lat) = sin dec × radius ÷ sin co-lat., which is the formula given. [अग्राया अक्षानयनम्] तेन हता ऽखार्कऽघ्नी क्रान्तिज्या लम्बकोऽस्य [य] (च्चा) पम् | तेन नवतिर्विहीना (यच्छेषं) तेऽक्षभागाः स्युः || ४० || Latitude from Agrā 40. Multiply sine declination by 120 and divide by the sine of amplitude. The sine of co-latitude is got. Find its arc in degrees. Deduct the degrees from 90. The remainder are the degrees of latitude. Now, sin co-lat = 120' × sin dec. ÷ sin amplitude. From this, the arc, co-lat is got. 90° − colatitude = latitude, as already stated in (IV. 28). From the formula of the previous verse, Sin amp = radius × sin dec ÷ sin co-lat, Sin colat = radius × sin dec ÷ sin amp. = 120' × sin dec ÷ sin amp. From the amplitude of the setting Sun also, the latitude can thus be found. The amplitude can be marked on a circle with the directions already marked by the observation of sunrise or sunset. 40a. A. हृता. A. खार्कघ्नी b. A1. कोस्य श्रापम्; (A2. स्प corrected to स्य) c-d. A. हीना छयेघतेक्षभागाः