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

XIII.33 XIII. SITUATION OF THE EARTH 257 Astronomical observation 30-32 Place a plank in a raised position, with its surface plane, as examined by dropping water on it. Set it so as to have its surface horizontal and level with the eye, and its parallel sides north-south and east-west. At the southern edge, in the middle, hinge a sighting tube (śaṅku) equal in length to the north-south length of the plank. With the eye at the hole of the rigid sighting instrument, at the hinge, lower the instrument so much, that the North-pole-star is sighted through the hole of the instrument. When lowered completely, (the observation) will be towards Laṅkā: when vertical it will be towards Meru; and lowered appropriately, it will be equal to the (local) latitude (as read) from the plank. Note. From the next verse we can understand that V.M. implies here that the north-south length of the plank is 120 units, so that the length of the sighting instrument also is 120 units = R. So taken, the perpendicular dropped on to the plank from the end of the instrument will be equal to R sine raised angle, and the base from the foot of the perpendicular to the hinge will be R cos. raised angle. तत्राऽवलम्बको यः सोऽक्षज्या तस्य शङ्कुविवरं यत् । विषुवदवलम्बकोऽसौ याम्योत्तरदिक्प्रसिद्धिकरः ॥ ३३ ॥ 33. When so sighting the pole-star, the perpendicular, dropped on to the plank from the end of the sight is the R.sine of the latitude of the place. The base so formed is the R cosine of the latitude of the place. The R cosine line, i.e. the base, coincides with the north south-direction line. Note. VM uses a table of R sines, taking R = 120 units. Hence the rule. Fig. XIII.1 [Diagram: A right-angled triangle representing a sighting instrument on a plank.

• The hypotenuse is labeled "Sight" and "R = 120 Units".
• The angle at the left vertex is labeled "θ".
• The left vertex is labeled "Hinge".
• The horizontal adjacent side is labeled "R Cos θ" and "Plank".
• The vertical opposite side is labeled "R Sin θ".] 30-34. Quoted by Utpala on BS 2.p.59. 30a. B. सभक्तता तुगं; b. B. फलर्क. C.D.U. दृष्ट्या c. A. कोद्यां; B. कोधां. A. शङ्कु; B1.2. शंशंकु d. A1.प्रंतिम; A2.प्रंतम; B.प्रतिम B. व्ययं व्यवस्थाप्य 31a. B.रुजुशंकु (B3.omकु) A.वुम्रथ; B. बुध्र्य b. B.नामये; A.C.D.नामयेत्. A2.शङ्कु c. B.शष्कुवम्रे d. A.B.C.D.ध्रुवतारादृष्टि 32a. A2.चेधो b. B.लम्बतया A.B.मूर्ध (B.र्द्धं) गेन (B.नं) तु c. A.चान्तराल; B.चान्तराला; C.D.चान्तराले d. A.छेधार्धसूत्रसमे; B.छेधृद्धं सूत्रसमाः (B2.समोः); C.फलकच्छांदार्धसूत्रसमे |; D.फलके भासार्थसूत्रसमे |; U.फलकच्छेदार्धसूत्रसमे | 33a. A.लंवोको य; B.लवको य b. A.B.सोरज्या; B.शकुविवरं यतं (B3.तं) c. A1.०लंकोसौ; B.लंडकोसौ