अथान्यत्राप्युक्तं । यदावैवहिर्विद्वान् मनोनियम्य इन्द्रियार्थांश्च प्राणोनिवेशयित्वा निःसङ्कल्पस्ततस्तिष्ठेत् । अप्राणादिह यस्मात् सम्भूतः प्राणसंज्ञको जीवस्तस्मात् प्राणोवैतुर्याख्ये धारयेत् । अचित्तं चित्तमध्यस्तमचिन्त्यं गुह्यमुत्तममं । तत्र चित्तं निधायेत तच्च लिङ्गं निराश्रयं ॥
XVIII. Symbolical Yoga Cult of Mudrá Or Chakra Diagrams.
Om the object of Yoga meditation, being already described in sections IX. &c. of this article as symbolical of Divine nature, and its different divisions as emblematical of the eternal attributes or hypostases of the Self—same Unity, they are as shown before, represented by the component letters of that mystic syllable, and meditated upon by the mental arithmetic of the speculative theosophist, the vedántist and yogi. But as the majority of people of grosser understandings are more dependant on ocular and sensible symbolism than abstract idealism, the Tantras have purposely contrived many a figure and diagram (Mudrás and Chakras) for their guidance, of which we will give a few below with their geometrical names and notations.
It will appear from the diagrams described hereafter that Om the symbol of Brahman the Universal Sat or existence, serves to show us as a chart of the world, or representation of the cranium, everything existing in the physical and intellectual world, which is expressed by the word Om (ॐ शब्द सर्ब्बार्थ वाचकः), in its different divisions and partitions for our meditation and contemplation. The pious and religious spiritualist may employ them in Divine contemplation, but the majority are at liberty to use them in the meditation of every other subject which comes to be comprised within the compass of their thought, in the groups of significations which the letters are said to convey. Hence the Yoga of old, meant only an intense application of the mind to all subjects of thought and knowledge. Thus the end of our Yoga philosophy is not only the abstruse meditation of Divine attributes, but the mental reflection of every thing besides.
XIX. Mathematical Investigation Into the Diagrams of Om.
Correctness of the Diagrams. We have seen from the diagrams given in the following section, that the Tántrika formulists have spared no pains to divide the great circle of the Universe, filled by the omnipresence of Brahma and represented by the figure om, into several parts for the purpose of meditating His different hypostases, and contemplation o£ the various orders of creation. We are now to inquire as to whether these several divisions of a mathematical circle of 360 degrees are geometrically correct, or mere arbitrary partitions made by ignorant priests for their own amusement and deception of their proselytes.
The Heptagon and Nonagon. Now for instance, the problem of inscribing a heptagon or a nonagon in a circle will at once startle a student of Euclid as altogether impossible, and identical with that which was celebrated among Greek geometricians as the problem of the trisection of the angle. If treated algebraically, it leads to a cubic equation with three real roots, the arithmetical value of which can be found only approximately.
The Lílávatí’s solution. The author of the Lílávatí has solved the problems, but given no account of the way in which he got the numbers stated by him; if they had been obtained by solution of the above mentioned equation, they would probably have been more accurate than they are. He only lays down an arbitrary rule, that the side of the heptagon is 52055/120000 of the diameter, and that of the nonagon 41081/120000 of the same. Neither of these is very far from the truth. The accurate value of the side of the heptagon lies between 82/182 and 105/242. The side of the nonagon lies between 13/38 and 105/307.
Commentators on Lílávatí. Among the commentators on Lílávatí, Rámakrishna, Gangádhara, and Ranganátha have not attempted any demonstration of the problems in question, and have contented themselves with merely repeating the figures contained in the text. Ganesa confesses that the proof of the sides of the regular pentagon, heptagon and nonagon cannot be shown in a manner similar to that of the triangle, square and octagon.
The Pentagon. But this is untrue of the pentagon; its side can be geometrically found as shown in Euclid Book IV. Prop 11; and the admission of Ganesa serves only to prove, that he was unacquainted with the Sanskrit translation of Euclid which contains a solution of this problem. Ganesa cannot mean only that the side of the pentagon is incommensurable with the diameter; for that is equally true of the triangle, square and octagon, inscribed in a circle.