On a stony surface made level as a mirror, describe a circle... at the center, place a gnomon twelve fingers high.
Modern Technical Commentary:
Defines the standard instrument for ancient observation: the Shanku (Gnomon). Its 12-digit height is universal in Siddhantic math, establishing a fixed unit for trigonometric shadow-to-angle conversions (cotangent relation).
On a stony surface made level as a mirror, describe a circle... at the center, place a gnomon twelve fingers high.
Modern Technical Commentary:
Defines the standard instrument for ancient observation: the Shanku (Gnomon). Its 12-digit height is universal in Siddhantic math, establishing a fixed unit for trigonometric shadow-to-angle conversions (cotangent relation).
Dimensions of the 12-digit Shanku used as the
fundamental unit for local height/shadow measurements.
The canonical gnomon length in digits (Angula).
[Ch. III, v.1]
Siddhantic Proof: Tri-Prasna (Shadows & Direction) v.1
Sanskrit (Devanagari):
अम्बुसंशुद्धे जलवत् समीकृते शिलाप्रदेशे ... तन्मध्ये द्वादशसंख्यकाङ्गुलानि स्थापयेत् ॥
Translation (Burgess):
On a stony surface made level as a mirror, describe a circle... at the center, place a gnomon twelve fingers high.
Modern Technical Commentary:
Defines the standard instrument for ancient observation: the Shanku (Gnomon). Its 12-digit height is universal in Siddhantic math, establishing a fixed unit for trigonometric shadow-to-angle conversions (cotangent relation).
Siddhantic Proof: Tri-Prasna (Shadows & Direction) v.1
Sanskrit (Devanagari):
अम्बुसंशुद्धे जलवत् समीकृते शिलाप्रदेशे ... तन्मध्ये द्वादशसंख्यकाङ्गुलानि स्थापयेत् ॥
Translation (Burgess):
On a stony surface made level as a mirror, describe a circle... at the center, place a gnomon twelve fingers high.
Modern Technical Commentary:
Defines the standard instrument for ancient observation: the Shanku (Gnomon). Its 12-digit height is universal in Siddhantic math, establishing a fixed unit for trigonometric shadow-to-angle conversions (cotangent relation).