Poorna Meemamsa Text Pages Booklet

7/27/2019 Poorna Meemamsa Text Pages Booklet

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better understanding; both the Bija and Samkhya are one and the

same as they are closely related to each other, for practical

purposes.

It is no wonder to a true aspirant on the path if it is sail that

these four forms, the Pada, the Bija and Samkhya, and the Rekha

are the keys of knowledge. Every aspirant, nay every student, nay

every Brahmachari, is initiated into the Holy Mantra, is given the

Holy Yantra as the very object of Worship, and is required to study

the Holy Veda. Bija and Samkhya fall under the category of Mantra.

To unveil the mysteries of Pada, Mantra and Rekha, three sciences

have been developed and entrusted to the care of the Brahma Rishis,

which are a mystery to the ordinary pale of students and aspirants.

The three sciences are technically called the Pada sastra, Mantra

sastra, and the Yantra sastra. Pada sastra has given birth to the

science, Grammar of Panini, Mantra sastra to the science of

Numbers, Arithmetic and Algebra, and Rekha sastra or Yantra sastra

to the sciences Geometry, Conic sections and Trigonometry.

The three sciences Pada sastra, Mantra sastra and Yantra

sastra, have each for their end and aim the presentation of the

fundamental Goal, the Brahma, bearing the nice harmony one with

the other among themselves. In one word these three sciences are

no more than three brilliant rays of light, proceeding from the same

fountain head of Light, nay three rays of brillian light converging into

the same Grand focus. The fountain head of knowledge, from

which the three rays of Science are proceeding and the Grand

focus into which the three rays of Science converge, is the Holy

Purna Mimamsa Darsana of Jagat Guru Sri Kalyanananda

Bharati Manthacharya Swami. Sringeri Sri Virupaksha Sri

Peetham.

readers, however grand their intellects may be So an exposition of

the Holy grand thoughts is essential, in the light of the Holy

Sampradaya of the Brahma Rishis, to facilitate the true aspirants on

their path.

Hence a short and clear commentary of the Darsanam will be

placed before the recipients.The commentary will be better equipped, if it is introduced with

a short dissertation, representing the way in which the three sciences

are focussed in the Purna Mimamsa.

Vedic Literature :- The whole of Vedic Literature has for its

end and aim the gist of two grand and holy teachings :- 1. The teaching

of Brahma Rishi Varuna, to his dutiful son Bhrugu, and 2. The teaching

of Brahma Rishi Uddalaka to his dutiful son Swetaketu. These two

teachings expound in full the fundamental Doctrine of the Vedic Lore,

in its systematic form, hence contain in them the rationale of each

and every query of each and every science. Both these teachings

proclaim in roaring voices that the multifarious objects (Bhutani)

perceived, evolve from the fundamental cause only without a second,

and that it is absolutely necessary for one to realise the fundamental

cause to realise the Highest Goal of Life, and that by the knowledge

of the Supreme fundamental Cause, one would acquire the

knowledge of one and all.

Objective World : The objective world, however variegated

and diverse it may appear at the very outset, is merely two fold in its

nature. 1. Nama (name) and 2. Rupa (Form). Under the Nama comethe Pada, Bija, and Samkhya, whereas Rupa is Rekha. Both the

Nama and Rupa are so closely linked to each other that the idea of

the one will not go without the other under any circumstances. Strictly

speaking, both the Nama and Rupa are only phases of one and the

same thing or object.

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Objective World, and verify the truth of the Vedic Doctrine. To be

brief, the phases of the Objective World are four and four only, Pada,

Bija, Samkhya, and Rekha. Thus We have before us, four Worlds,

to all practical purposes, 1 The Pada World, 2. The Bija World, 3. The

Samkhya World, and 4 The Rekha World. Hence let us take one

World after another for our observation.

Rekha World : Of the four Worlds, Rekha World is the foremost

to be taken into consideration, for the reason that it represents the

form perceptible of the Objective World. The perceptible form is

technically called the Rupa, and the graphic representation of the

Rupa is technically called the Chakra, (the figure). It is no Wonder to

any observer that a good number of Chakrams of various

descriptions are worshipped every day by worshippers of Veda, as

the very forms of the Deity which they adore. These Chakrams, the

very objects of worship of various descriptions, are here technically

called the Rekha World. To place before our readers, the grandeur

of the Rekha World, as the very prominent means to realise the

Highest Goal. We herein expound the mysteries of the simplest

forms of the Chakrams, that are within the ordinary reach of one and

all. The simplest forms of chakrams are technically called, 1. Bindu

Chatushtaya, 2. Pancha Kona, and 2. Shat Kona. To all practical

purposes, these Chakrams should naturally inclosed in a Circle,

which is technically Called Maryada Vrutta (bounding circle) Thus

we have before us.

To understand the mysterious knowledge which these

chakrams graphically represent, one should have a clear knowledge

of the Tittiriya Upanishat.

Gist of Tittiriya Upanishat :- Varuna taught to Bhrugu, that

these perceptible Bhutani, commencing with Brahma (Prajapati) and

otherwise termed Atma) Akasa evolved; from Akasa, Vayu; from

Vayu, Agni; from Agni, Apaha; from Apaha, Prithvi; form Prithvi herbs;

from herbs, Annam (Food); and from food evolved into Rethas,

evolved the Purusha - the perceptible corporeal Rind with head,

hands, trunk and legs. And this Purusha is said to be the final product

of evolution from Atma or Brahma. To avoid confusion andmisconstruction, Mother Sruti, with the tip of the pointed finger, is

pointing out the Purusha thus :- This is the head of that Purusha, this

is the right wing; this is the left wing; this is the atma (Middle); and

this is the tail. Thus the perceptible human form is pointed out by

Mother Sruti, as consisting of five parts, akin to the five parts of a

bird - head, two wings, body and tail. To understand the similarity in

the human form, a little nicety in the arrangement of the human form

should be observed.

Arrangement of the human form :- Let the Observer, calmly go

alone, and lie flat with his back downwards, and face upwards, upon

a vast sandy plain, with head towards the East, and feet towards the

West. And then let him open his eyes wide, and observe on all sides

around him with a Mathematical Intellect. It goes without a saying

that he feels himself to be at the centre of one and only one Circle

without a second, with the Horizon as the Circumference.

N.B:- It is this observation of the first Geometrician, that blessed

him with the conception and definition of the Circle.

Posture 1:- Let the Observer place his right palm close to the right

hip joint, and the left palm close to the left hip joint, with the hands

lying flat on the ground, bulging like a bow; and let the legs also be

placed flat on the ground, with the feet touching each other face to

face.

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middle Atma, and the legs the tail. Now, let the observer draw a nice

graph of his own posture, as directed herein - Commencing with

Brahma Randhra, (the centre of the head) passing through the left

arm-pit, touching the left side and knee-cap, the central fingers of

the feet, right knee-cap and side, and passing through the right

arm-pit to Brahma Randhra. This graph, if nicely traced with a littlemathematical intelligence, would assume the form of an Ellipse. Let

another be drawn from the centre of the net, passing along the left

shoulder, elbow and palm, touching the Linga (penis) and passing

along the right palm, elbow and shoulder, to the centre of the neck.

And this graph too, assumes the form of another Ellipse. Thus the

whole graph appears as if it were made up of two Ellipses cutting

each other cross-wise. The figure clearly exhibits the five portions :-

1. The head, 2. The right wing, 3. The left wing, 4. The body and 5. The

tail. It is plain that this figure is the graphic representation of the

Annamaya Kosha or the Sthula Sarira. This figure can as well

represent any of the other Koshas, for the reason that every Kosha

is described by the Sruti, as consisting of the same five parts, though

with relative characteristic Significance; further meditation of the other

Koshas in the light of Brahmavalli, would gradually lead the observer,

to forget, rather neglect the 4 koshas, Annamaya, Pranamaya,

Manomaya and Vijnyanamaya, and identify himself with the

Anandamaya kosha, when he thinks of himself as having the 4 points

of his form huge the Brahmarandhra, the tips of the right and left

elbows, and the tip of the central fingers of the feet, touched and fourcardinal points of the Huge Circle, whose circumference is the

Horizon. And this is no more than the Chakram, No 1. In brief this

figure, or Chakram, is the graphic representation of the Microcosm,

(Purusha), as taught in Brahmavalli. Microcosm is an epitome of the

Macrocosm nay Macrocosm is analogous to the Microcosm. So

are authorised to worship the Purusha of the Purusha Sukta.

Posture 2 :- Let the observer, now straighten his hands a little, and

place the tips of the middle fingers of both the hands a little near the

knee-caps on both the thighs. And let a nice graph be written as

directed :- from the Brahma Randhra trace the course along the left

shoulder joint, elbow, knee cap tips, of the middle fingers of the feet,right knee cap, elbow, shoulder joint, to the Brahma Randhra. Now

the course of the mathematical line would place before the observer

a fine Ellipse. Now let the observer conceive a straight line, passing

through the three points - 1. Brahma Randhra, 2. Muladhara (Annus)

and 3. Tips of the middle fingers of the feet, and another straight line

passing through the navel, perpendicular to the above, crossing the

elbows both ways. These straight lines are called the axes of the

ellipse. Let the two straight lines be produced both ways to meet the

horizon. They would naturally touch the cardinal points of the Horizon.And the wonderful feature of the ellipse under consideration,

The navel (Manipura) is the centre, whereas, the Swadhishtana (near

Linga), and Anahata (near the heart), are the two foci : - or Muladhara

(near the annus), and Visuddha (near the collar), are the foci. A little

more meditation of the Pranamaya, Manomaya Vijnyanamaya, and

Anandmaya Koshas, in the light of the Brahma Valli, would make the

observer feel highly astonished to see the wonderful Confocal Conics

flash before him in dazzling colours. The Horizon, the circle, the five

koshas the Ellipses, and Sushumna, the line ellipse. Thus thefollowing equation of a system of confocal conics is favoured by

Brahma Valli :-

x2Plus

y2 = constant (1)

a2 + b2 +

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either side should be in the same straight line with the Brahma

Randhra. The two straight lines should resemble to all practical

purposes the two equal sides of an Isosceles triangle. Let the right

palm be placed on the right teat, close and the left palm upon the left

teat with the elbows straightened. A nice mathematical graph of this

posture would bless the observer with the Chakram, 2. This chakram

also exhibits the pentafold classification of Brahma Valli, in another

way; hence can be deemed as another representation of the Purusha,

the Microcosm. This Chakram is generally worshipped by those

who worship the Purusha in the form of Siva.

Chakram 3 :- The Shatkona is widely known as the Sudarsanam.

The word 'Darsanam' means a clear exposition of Philosophical

truths, nay the doctrines of Philosophy. The prefix Su means perfect

or complete. Hence Sudarsanam means perfect and clear exposition

of Upanishadic Philosophy. This Sudarsanam is revered as the veryChakram, which Bhagavan Sri Krishna holds ever and anon, in His

right hand. It goes without any say that Gita is the perfect Darsanam

of Sri Krishna Bhagavan, in the form of Pada, whereas this Chakram

is the Darsanam of Sri Krishna Bhagvan in the form of Rekha. Hence

the whole of Bhagavat Gita, is merely an exposition of this

Simple Chakram the Shatkona, nay, this Shatkona is Gita in a

nut-shell. Such is the grandeur of the various Holy Chakrams that

have been the objects of worship from time immemorial in India.

Mathematical Significance :- All these Holy Chakrams appear toall practical purposes, as if they were formed by the combination of

the Mathematical figures to be seen in Geometry and Conic Sections,

in harmony with the Mathematical laws. Hence close study of the

light of the Mathematical laws would make the students of Philosophy,

realise the lofty philosophical problems easily without any confusion,

out of the Shatkona (Sudarsanam), while the Panchakona

contributed to the development of Conic Sections. Every

Mathematical wonder and rarity is no more than the

representation of some philosophical truth or other; and every

Mathematical Problem is no more than an image of some

philosophical problem or other.

Vedanta and Figures:- It is said that the Mathematical figures have

had their bir th from the philosophical (Vedantic) conceptions; and it

will not be out of place, if a few illustrations are shown in favour of

the argument. The fundamental plane figures of the Mathematical

Science are 1. The Point, 2. The straight line, 3. The angle, 4. The

lateral, the type of which is the Euailateral triangle, and Square, 5.

The Circle, 6. The Parabola, 7. The Hyperbola and 8. The Ellipse. In

strict logical sense, these eight, rather nine forms, can be termed

the Conics, or Conic Sections. What is a Conic, or Conic Section,then? Conic Sections are the figures formed by the outlines of the

cut surfaces, when a cone is cut by a plane. What is the Cone, that

ever stood before the first Geometrician, to have a copy of all the

figures, necessary for the building up of his Science? It is no more

than the Majestic and Holy Cone, that has been the object of

Worship of holy sages in Aryavarta, from time immemorial;

which is generally revered as The Sri Chakra, Meruprastara.

From this definition of the Conics, we can very easily conceive,

that all the Mathematical figures have had their origin nay, birth,from a single form, the cone. Hence the Cone can be easily

realised as the fundamental cause of all the Scientific figures,

of multifarious kinds. Even the highly polished definition of the

conic, bears testimony to the same fact. The definition runs thus :-

"One definition which is of especial value in the geometrical treatment

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eccentricity, determines the nature of the curve; if equal to unity, a

parabola; and if less than unity an ellipse. In the case of a circle the

centre is the focus, and the line at infinity the directrix; we therefore

see that a circle is a conic of zero eccentricity."

The definition of a conic in projective geometry, leads us to still

more wonders. A conic section is defined as the projection of a

circle "the particular conic into which the circle is projected depends

upon the relation of the Vanishing line" to the circle; if it intersects in

real points, then the projection is hyperbola, if in imaginary points an

ellipse, and if it touches the circle, the projection is a parabola. From

this it can be fairly argued that the conics have had their origin,

rather birth, from the circle and circle alone. It can as well be

argued that the lateral figures, also have had their origin, from

the circle and circle alone. It is a well-known problem in the

science, that the circle is only a polygon of N sides. Polygon

means many-sided figure. Many means more than one in

vernaculars, and more than two, in classics. By substituting

the values, 2,3,4,5 and so on, to N, we reaslise, one after another,

an angle, a triangle, a quadrilateral, a pentagon and so on, the

various figures of the science. If solid be taken into

consideration, the cone stands as the fundamental cause of all

the figures; and if plane be taken into consideration the circle

stands as the fundamental cause of all the figures. Whether it

is the solid or the plane, it is immaterial, for the seekers of Vedic

knowledge. It is sufficient if they can realise that the fundamental

cause of all the forms is one, and only One, without a second.

They can as well realise that Brahma, the Purnam is the

fundamental cause of all forms perceive; and that Brahma is

One, and One only without a second.

1. The Point :- The point stands for Avidya, Avidya is deemed

as Midhya. Midhya is that which has no positive existence, but

appears to exist for the time being. A point is defined as that which

has no parts or which has no magnitude. To all practical purposes,

a point has wide application in the science, but in its real aspect, it

displays no single property of a figure, which is expected to have

some dimension, or other for it to be taken into consideration. Hence

the mathematical aspect of the point is a mere echo of the Vedantic

aspect of Avidya midhya. The equation, that the point is a circle

with zero radius, also corroborates the same Vedantic Law.

2. Straight Line :- The straight line represents the Guna. The

conception of the straight line is derived from the popular "guna"

which means the string of a bow. Guna in Vedanta is any one of the

three, Satwa, Rajas, and Tamas, which are considered as the

component parts of Prakruti. Straight line is a fundamental illustration,that bears testimony of the Law of Adhyasa (Superimposition), of

the Vedanti. It is the fundamental illustration that brings to the mind

of the observer, the conception of Adhyasa, in a concrete form

perceptible to the same eye. The observer sees the horizon circular,

that is completely curved. Hence any part of the horizon, should

naturally be a curved line being the part of the curvature. But the

observer perceives only a straight line, between any two points of

the horizon, within a short range of observation. It is this observation

that had led the first scientist to frame his problem "That a circle is a

polygon of N sides. Now what is the figure that is within the range of

the observer who perceives the horizon complete in one range of

observation? It is no more than the plane figure, circle contained by

one line horizon, which is called the circumference. What is that the

observer feels in his second observation, with reference to the same

figure? A polygon of N sides. How can it be possible for one and

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If one is correct, the other is false. As far as direct perception is

taken into consideration, one curved line is the reality; hence, N sides,

is mere superimposition. Yet Superimposition is not without purpose.

Along the reality, superimposition works hand in hand with the reality

to facilitate the Yyavaharica (the worldly life), and to realise the

mysteries of the Paramarthica (The Reality). It is only through thesuperimposed straight line and the polygon that we have to realise

the various measurements of the curved figures. One word of

importance with reference to the superimposition of the straight line.

the observer perceives the circular space and the horizon directly,

but observes not any point or straight line, to present him with the

ideas of a point, the centre, or a straight line, the radius or the diameter.

The definition of the circle, clearly shows the superimposed nature

of the point and the straight line. A circle is a plane figure contained

by one line which is called the circumference, and is such that all

straight lines drawn from a certain point within the figure are equal to

one another. Here straight lines are said to be drawn; hence, they

are nothing but; the work of human superimposition. And similar is

the case with the point which is described as a certain figure. Hence

the centre, the diameters, the cardinal points on the

circumference (Horizon) and the radius are no more than the

work nay superimposition of the scientific thought.

3. Angle:- Strictly speaking, the Angle stands for the Guna

of the Vedanta. It is for the reason that the angle is the inclination of

two lines, that the lines, also are reckoned as the marks, nayrepresentation of the Gunas. The classic name, Gonia for the angle,

shows clearly the real origin and significance of the figure. The Greek

Gonia is a simple derivative of the Sanskrit Kona; and kona is the

Vedantic representation of the Guna. We may even think that the

term Gonia is a directive of the term Guna itself.

means the congregation of the three guna,Satwa, Rajas and Tamas.

Prakuti is defined as being made up of the three gunas. Hence

Triangle equilateral stands for the Vedantic Prakruti.

5. The Square :- The square stands for the cardinal points of

space. It is called Bhupura; and Bhupura means the plane

superficies, with regular dimensions, and boundaries.

6. The Circle :-Circle is said to be the fundamental cause

of all figures; hence it should naturally stand for Brahma, the

Purnam. What is the Circle? It is the maximum space that falls

within the range of observation complete, on the plane superficies

of the Earth, with horizon as its boundary. And this space is called

Akasa. It is no wonder if it is said that the Circle represents aptly

this Akasa visible. Tittiriya Sruti proclaims that Brahma is that

which has Akasa for his body - "Akasasariram Brahma". Another

Sruti speaks of the Brahma as "Gagana Sadrusam", (resembling

the Akasa) And visible Akasa is the Circle. Hence the circle is no

more than Brahma the Visible. That is why the Circle is termed

the Purnam, in Sanskrit, a synonym of the word Brahma, so that

it may serve the two-fold purpose, the Vyavaharica, in the Science,

and Paramarthica, in Vedanta Philosophy.

Strictly speaking, the Circle is the only available form, by which

Brahma can be realised. It is the representation of the Visible

Brahma, and not of the Real Brahma, which is above all planes of

perception, and representation. For the reason that the Circle is the

representation of the Visible Brahma, it is the nearest possible

representation of the Real Brahma. Visible Brahma is technically

called the Iswara, so that the observers may keenly realise the

distinction between the two forms ofBrahma, the Visible, and the

Invisible.

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This Avaranam is two fold Maya and Avidya in the View of certain

sages. Then the circumference of the circle represents the Maya,

Whereas the circumference of the Ellipse, the Avidya. Here the

readers should not confound the Avidya, genus, with Avidya,

species. This Avidya is deemed as the Avaranam of the Jiva, in

contrast with Maya, which is deemed as the Avaranam ofIswara.The singularity of the Circle bears testimony to the Oneness of the

Iswara, and the variety of the Ellipses to the manifold variety of the

Jivas.

Parabola, and Hyperbola, too as the projections of the circle,

similar to the ellipse, can be easily realised as the representations of

some forms of Avidya, after the manner of the ellipse, hence they

can be very easily argued as the Avaranams of some forms of Jivas

(Living beings).

This Avaranam is generally called the KaranaSarira of theIswara, as well as of the Jiva. Variety in the Jivas, (Living Beings) is

due to the variety of Avidya, the jiva-karanam, and the Oneness of

Iswara is due to the singularity of the Iswara Karanam, the Maya.

And Brahma Supreme is above all conception, and representation.

So far with reference to the Rekha World; the Rupa, for the

present. Now let us proceed to the Pada World, the plainest and

foremost of the Nama.

The Pada World:- The Pada world is twofold - Sruti and Smruti.

Sruti is the Cause, and Smruti,the Effect. Sruti is otherwise calledthe Veda. It is Nitya Apourusheya, and Swathahpramana. The

real nature of the Sruti should be known only through the Sruti.

Smruti is Anitya. Pourusheya, and parathahpramana. Both the Sruti

and Smruti are revered as the highest authority of Knowledge.

Let us see what these highest authorities of Knowledge proclaim.

Yedichechanto Brahmacharyam charanti Tat the Padam

samgrahena bravime - "Om ityetat'.

Here the word 'Padam' means the word, and the Sthana (place).

This 'Om' is said to be the Brahma, as well as the Sarvam. "Omiti

Brahma, Omitidam Sarvam."

Vedanta Darsanam of Bhagavan Krishnadvipayana Bharati,

Veda Vyasa, proclaims for ever that the holy Literature of Aryavarta,

the Sruti and Smruti, have for their end and aim, only the Brahma.

This can be realised from the opening sutra of the grand Darsana

"Athatho Brahmajijnyasa."

Bhagavan Narayana, (Sri Krishna) proclaims through His world

wide Smruti, the Gita, the "Aham" is the fundamental goal of all the

Vedas - "Vedaiseha sarvairahameva vedyaha." And that Brahma

is represented by three words - "Om, Tat, Sat". "Om Tat Sat iti

nirdeso brahmanaha trividhaha smrutaha."

A close observation of the above, and similar other statements

of Sruti and Smruti, will make the observer that the fundamental Goal

is specially represented by the three Holy Words, 1 Om, 2. Brahma

and 3. Aham, and generally by a good many words, the prominent

of which are as follows :-

1. Purusha, 2. Sarvam, 3. Ananda, 4. Dahara, 5. Sarira, 6. Rasa,

7. Gati, 8. Siva, 9. Pranava, 10. Pada, 11. Aja, 12. Atma, 13. Sat, 14.

Bhuma, 15. Karta, 16. Ishte, 17. Garbha 18. Yajnya 19. Swapiti 20.

Purisaya 21. Prajapati 22. Taraka 23. Tat, 24. Purnam, 25. Turiya 26.

Param, 27. Gayatri, 28. Yantra, 29. Chakra, 30. Sudarsanam.

All these words are synonymous, with the Word, Brahma, or

Om, to express whose connotation, the holy Sruti and Smruti, have

been ushered into the World.

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Smruti, have for their final Goal the two Sacred Mantras, the Pranava,

and the Gayatri : "Om itit idam Sarvam" - "Gayatree va idam

Sarvam." "Om ityekaksharam Brahma."

Origin of the Nama :- It is no wonder if it is said that both the

Pada and the Bija worlds, whatever their relative significance, may

be, are only the outcome of the combinations of the letters in the

Sanskrit Alphabet (Akshara Samamnaya). The Akshara Samamnaya

is two fold - 1. Narayana, and 2. Maheswara. Narayana Samamnya

consists of the eight groups (Vargas), commencing respectively with

the letters : A ka, Cha, Ta, Tha, Pa, Ya, Sa and they are as follows :-

n } TT T @ z W n+ n' K > |T v, ## sa x s & & D


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y p y jy

nanarupa." Sri Krishna Bhagavan proclaims the same, thus -

'Aksharanamakaosmi." The grandeur of this Akara can be better

understood from a close observation of the System of Panini's

Grammar.

Panini's Grammar :- Panini's Grammar is the Summum bonum

of Sanscrit Language. There is no word of Sanscrit, which can escape

the sphere of Panini. The work, really commences with the

Maheswara Sutras, fourteen and closes with the Sutra 'AA'. As

such the whole work has for its beginning, the Swara, (vowel) 'Aa',

and for its close, the Swara 'A'. This arrangement of the whole work,

within the two Swaras, is a mere copy of the arrangement of the

Veda, which has the same Swaras, for its beginning and its end, as

taught by the Sruti " Yo Vedadow Swarah procto Vedante eha

pratishtitaha; tasya prakrutileenasya yah ParassaMaheswaraha."

"AA" :- The closing sutra of Panini is intended to convey that

there is One and only One Akara. Samvruta, which is above the

sphere of his Language. The position of the sutra itself shows that

this Akara is the Root, nay, Bija of the whole Language. This Samvruta

Akara is the Varna? (letter), that represents Brahma. With reference

to Language, it exhibits the same relation, which Brahma bears to

the Universe. Brahma is above all the objects of the Universe,

but blends with all the objects to give them stability. Similarlythis "Aa", keeps itself aloof from the Words of the Language, giving

potency to all the letters for their stability of pronunciation. Without

the aid of this "Aa" no letter of the language, can be really pronounced,

It is highly astonishing, and wonderful to hear that a single letter "Aa"

has given birth to the various letters of the Varnasamamnaya, the

g

Bindu and Visarga :- Two vowels are seen in Sanscrit, which

display wonderful features, they are, the Bindu and the Visarga.

These two cannot be pronounced, as they are, under any

circumstances, individually, but should be aided by 'Aa'. In brief,

they are nothing without the aid of "Aa(n)" but display wonderfulphenomena, under the support of"Aa(n)". As such, they represent,the Prakruti, and the Vikruti, respectively. The word "Aham" is no

more than the combination, of the three vowels, Akara, Visarga

and Bindu. From this it can be realised that the Aham is a compound

of the three, Brahma, Prakruti and Vikruti.

Sankhya World :- Sankhya World is a simple, rather general

form of Nama. It is the connecting link between Pada, and Rupa.

The Samkhya world has for its purpose the exposition of the variety

of the Rupa in relation of Nama. To be brief, Sankhya stands midway

between the Akruti and Vyakti. Hence it serves the purpose of

explaining the relation between the Genus and the Species, or the

cause and the effect. Vedic Language is so mysterious, that every

word of it, nay every letter of it, has a peculiar numerical value. Some

words are very popular as referring to numbers, while every letter

has its special number of represent. The relation between the letters

and numbers is plainly seen in the Aphorisms, "Kadi Nava; Tadi

Nava;Yadyashta; and Padi Pancha." These Aphorims are not

merely conventional, but are quite natural and scientific, that by theapplication of these values of the synonymous nature of different

words can be easily realised, It is by this mysterious relation between

the Sanscrit letters and the Numbers, that the Divine Glory of the

Vedic Literature can be easily established. The above aphorisms

have for their support, a good many Vedic Equations. The inseparable

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numerical importance of the Mantra. Hence the investigation of the

mysteries of the Samkhya world are not of little importance in the

field of Vedanta. Let us therefore observe the general features of the

Numbers, a little, and see how far the Doctrines of Vedanta, are

corroborated by the Science of Numbers. Hither to, we haveobserved that all the Mathematical figures, are only the modifications,

rather superimpositions upon the Circle, as such the Circle is the

Main Causes of all the figures. And similarly the whole Pada World,

has for its focus the Word Om. If we can see a number that is the

fundmental Cause of all the Numbers, then our ambition will be fulfilled

to the very letter. It requires no proof to say that all the Numerical

World, however majestic and grand it may be, is only a modification

of the Nine Integers, and the Zero. There is also another Number

which is called the Infinity, which is above the pale of all calculations.

This number Infinity, is called "Param" or "ara", which is also a

prominent word, that stands for Brahma. The word "Param" exhibits

a peculiar status in Sanscrit. It is used in the three Genders, with

characteristic Significance. Masculine "Paraha" represents the

Purusha (The Man), who conceives himself as the "Aham", and who

is called by the Vedic Sages, the "Pranava." Feminine "Para"

represents the Number Infinity; and Neuter "Param" represents the

Figure. Circle. Above all Vedic Param represents the Brahma

Supreme. Hence the Number Infinity should naturally represent

Brahma.Purusha :- Purusha is called Pranava by the Sages for the

reason that the Sruti "Navo navo bhavati Jayamanaha", calls the

Purusha "Navaha." Neuter "Nava" is Number Nine. Hence Number

Nine represents the Purusha, the Prajapati, the Iswara, the First

Man, and the Man, as well. But the Purusha thinks of himself as the

Rupa, together with Bindu", the word is also indicative of the Holy

Idea that I am "Ekadyashtantarupa", together with Zero. Thus Aham

is the fountain Head of all the letters of the Sanscrit Alphabet as well

as that of all the numbers of Arithmetic. Aham has a twofold

significance, the significance of a word, and the significance of aletter. There is the usage of the word Ahmkara, in Sanscrit.

Ahamkara means the letter Aham, when the whole of Aham should

be treated as a single letter. Similar is the case with Om. Om is a

word and a letter. It is also called Omkara. When Om is taken as a

word, it should be considered as being comosed of the three letters,

A,00? and Ma when it means the Purusha, or the Prajapati, the

Apara Brahma, the Cognizable. When it is considered as a letter

Vedic, it is Only one letter, that stands as a mark for Brahma, the

Supreme. When Om is a word, its numerical value is 135, which is

equal to Nine. If it is taken as single letter, then it represents the

Para, hence its numerical value is Infinity. Similarly, the values of

Aham are twofold. If Aham be a word, then its numerical values are

180 or 90, 18 or 9. If it be a letter, its numerical value is Nine, only.

And this value of Aham is in harmony with the dictates of the Sruti

"Navo navo bhavati Jayamanaha", and the Smruti "Tasya

Vachakaha Pranavah."

Development of the Science :- It is this wonderful value of

Aham, 180 that has given birth to all the fundamental principles of

Mathematical Science, a citation of a few of which, will not be out ofplace. Number 18 has given birth to the eighteen place of Aryan

Numerical Notation, namely 1. Eka, 2. Dasa, 3. Sata, 4. Sahasra,

5.Ayuta, 6. Laksha, 7. Prayuta, 8.Koti, 9. Arbuda, 10. Abja, 11. Kharva,

12. Nikharva, 13. Mahapadma, 14. Sanku, 15. Jaladhi, 16. Antyam,

17. Madhyam and 18. Parartham, with a tenfold multiplicative

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It is this 180, alone that has given birth to the conception of the 180

degrees of the Parartha, (Hemisphere) and the 360 degree of the

Celestial Sphere, the Circle. Similar is the case with the Ninety

Degree of the Right Angle and so on.

Other Numbers :- Now that we have found out the Numberrepresenting Iswara, the development of the other numbers can be

easily traced. It is said that Iswara wills that He should multiply,

("Sokamayata Bahusym"). So by multiplying Nine with Nine, we

get all the numbers one after another, or by the splitting of the Nine

after the fashion of Aham (18), we get right kinds of pairs, wherein

we see the evolution of the eight integers, only. In the highest

philosophical sense, every Integer is only a superimposition upon

the Number Nine, for the reason that behind every number we

can trace out the existence of Nine. This can be better understood

by means of illustration, thus - Take the number two, for example,

Split up 2 into its component parts, then 2 equals 11; which is 9 plus

2. Thus we see 9 behind the 2. In this way every number can be

proved to have 9 behind it, 3 equal 12 or 21. Divide the numbers by

9 and you will see the remainder, 3 only. Again 4 equals 13, 31 or 22,

Divide the numbers by 9, and the remainder is 4 only. The aw holds

good to all the numbers, without any exception. In considering One,

we should split it up as 10; and we get 1 as remainder. This system

is in harmony with the teaching of Bhagavan, "Iswarassarva

bhutanam hruddeserjuna tishtati."Zero : It is generally called the Cipher (Sunyam). It is two-fold,

in its nature, one representing "Absolute nothing, whereas the other

a "Negligible quantity. The equation (a/a) equals 1, bears testimony

to the value of Nothing; and the equation (a/o) equals infinity to the

value of the negligible quantity. Both these values are pertinent to

mysteries of the Samkhya world, as well as the mysteries of the

worlds, Rekha; Pada; and Bija, let us summarise in brief the gist of

the above so that the harmony among the different worlds, and the

harmony of the different worlds with the Real Vedic Knowledge, may

be realised to the full.Rekha Samkhya Pada Bija

1 Circle, plain Infinity Brahma Param Om&A (Aa)

(Samvruta)

2 Circle & Centre Nine (9) Iswara Aparam Om&A (Aa)

(Vivruta)

3 Point Cipher Avidya Sakti Bindu (0)

4 St. Line One (1) Guna

5 St. Lines Parallel Two (2)

6 Angle Three (3) Guna Sa; Ta; Ra7 Equ. Triangle Nine (9) Prakruti Hreem

8 Square Twelve (12) Maya Hreem

9 Rhombus Twelve (12) Avidya Hreem

10 Ellipse Eight (8) Bhuta or Kosa

11 One (1) Akasa Ha

12 Two (2) Vayu Ya

13 Three (3) Agni Ra

14 Four (4) Apaha Va

15 Five (5) Pruthvi La

16 Six (6) Oshadhis17 Seven (7) Annam

18 Eight (8) Rethas

19 Nine (9) Purusha Aham

20 Cone Infinity Brahma Om

21 Circumference Infinity Avarana

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Ananda; Sarira; Rasa; Gati; Pada; Aja; Bhuma; Karta; Ishate; Yajrya;

Turiya; each equals to Nine (9).

3. Brahma; Prajapati; Viswam; Sarvam; Dahara; Swapiti; each

equals to Eighteen (18).

4. Chit; Tat; Jiva; Deva; Atma; each equal to Twelve (12).The relation between Pada, Bija and Samkhya can be realised

from the following:-

Pada Bija Samkhna

1. Veda Pranava & Gayatri (9) & (24)

2. Ramayana Shadakshari & Gahatri (6) Kandaas & (24) 000, Verses

3. Bharata Aham & Param (18) Parvams & (1) 00000 Verses

4. Bhagavata Dwadasakshari & Aham (12) Skandhams (18) 000, Verses

5. Gita Aham & Saptakshari (18) Cantos & (7) 00, Verses

Conclusion : A close observation of the four worlds would

clearly show how each of them have had their birth from one and

Only One Real cause, Param, Brahma, Purnam, which has

manifested into the four forms;- 1. The Circle, 2. The Infinity; 3. The

A(Aa), and 4. The Om. It can as well be observed that every lateral

figure can be raised to the status of a higher figure, or lower one, by

Revolution, positive or negative, and that every number can be raised

to the status of a higher number, or lower one by multiplication or

division, the final evolution being the Circle, or the Infinity, and thefinal involution being, the Point, or the Cipher. It is an admitted fact

that the Real Cause is Purnam. Infinity; and the Effect, the World is

perceived to be Purnam, Infinity. This Objective Purnam, is the effect

of the Real Subjective Purnam. Hence, the Microcosm, the

Macrocosm in a nut-shell, can as well be said to be Purnam. If the

- "Purnamadaha Purnamidam Purnat Purnamudachyate; -

Purnasya Purnamadya Purnamevavasishyate"

Consequence : Sruti 'Brahmavit Brahmaiva bhavati',

proclaims that the knower of Purnam, become One with Purnam,

and enjoys Supreme Bhss Eternal. Hence Purna Mimamsa is

absolutely necessary. Hence a brief common ary of it will be

commenced. Om.

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by

Jagadguru Sri Kalyanananda bharati MantacharyaSwami Maharaj

Terror of Theosophy & Defender of Vaidika Dharma

Sutra 1 : Adhatah Purnajijnyasa

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Purnam is defined as the Substratum of superimposition of all

the figures or forms. The substratum of figures is called the

Superficies in Mathematics. Superficies is only desbribed in a general

way by the scientists and not any special attention is paid in its special

nature. The general conception of it is that it is some space with

only two dimensions, length and breadth, without any consideration

of thickness. Even though it is considered as space having the two

dimensions, the real form of it is not all described, hence the

conception seems to be weak. If it be defined as space without

thickness or height, it would be more sound. A wide range of

observation, convince us that the Cone is the Substratum of all the

figures; but the Circle can be realised as the very Substratum of all

the forms, plane, that have their status upon the Superficies.

Now that the Chakram is defined as the graphic representation

of some idea or the other, by means of lines. It excites one's curiosity

to know whether the Purnam can be represented, by any chakram;

and to satisfy such curiosity, the next sutra is introdued.

Sutra 4 : Taddhi Vruttarupam

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'Tat' means that; 'Hi' is an interjection indicative of surety'Vruttarupam is a compound of the words :- Vrutta and Rupa. 'Vrutta'

means the Circle, and Rupa, the form' the term as a whole means

"That which has the form akin to that of a circle. The sutra means

'That-purnam is surely of the form which is akin to that of the circle.

The surety is the proclamation of the Sruti, "Akasasariram Brahma",

thickness, that is the plane superficies perceptible to the human eye,

is simply circular; as such the Akasa visible to the eye, can aptly be

represented by the Circle; nay the circle is only a representation of

the Akasa, visible and notheing more. For the reason that the Sruti

proclaims that Brahma has Akasa for its body Vedic scholars picturedBrahma, the Purnam, by the Circle. Hence the circle is the only

figure that can stand as a mark or representation of the Purnam. We

can as well realise that the plane Superficies, can also be represented

by the Circle, so far as the visible form is taken into consideration.

Hence, to think of the superficies as having two dimensions, length

and breadth, is rather a mis-conception, and superimposition. If the

superficies is conceived to have two dimensions, then it would be

represented by a squae, whose form is absolutely imperceptible in

Nature; for the reason that Nature presents everywhere; only a circle

and not any other figure. It is only upon the visible superficies circular,

that the square form, with equal dimensions of length and breadth

has been superimposed; hence the first observer was puzzled to fix

any form for his superficies and that is the reason of silence on the

part of all the Scientists even to present day with regard to the

question.

The curvature of the Sky :- The plane superficies, within the

range of complete human observation, appears circular, with the

Harozon, as the circumference; and the complete space, within the

range of observation, merely spherical, the form being a hemisphere.

It is highly curious to know the why of the curvature. The unhindered

rays of light proceeding from the Antahkarana of the observer,

proceed uniformely throught the Eye in straight lines, as far as

possible, and stop at a distance, when they are incapable of further

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is called the circumferene, and is such that all straight lines of light,

proceeding from a certain point, Antahkarana, within the figure to

the horizon, are equal to one another. It is Universal that the Horizon,

is a single curved line, and the vault of the Sky, a curvature,

resembling a hemisphere, with the superficies of the Earth as theBase. This special hemisphere is due to the highest possible

expansion of the Antahkarana, through the Eye. It is the light of

Antahkarana, that is obstructed on all directions, that makes the

observer feel the maximum space within his complete range of

observation, a hemisphere. It is the weakness, of the human

perception through the sense of vision, that is the cause of this

hemispherical conception unreal, of the unlimited space, and nothing

more. Yet the ignorant think it to be true.

Weakness of other Senses :- It is clearly shown that the sense

of sight, the foremost of all the senses is absolutely week; and as

such perceives only false state of things. It can as well be observed

that the other senses are equally weak in their perceptions, presenting

unreal perceptions and forms only. Hence one should not entirely

depend upon one's own perceptions of the senses, but correct

them throught higher knowledge of the Sruti and Smruti.

It is said that Purnam is represented by the Circle; and the

circle is defined as a plane figure, contained by one line which is

called the circumference. And human perception of sight is said to

be weak. The weakness of the observation can be plaintly realised

by another observation of the same thing in a higher plane. In the

higher plane, the circle is proved to be a polygon on N sides, the

sides being straight or curved, as the observer perceives; when the

circumference is not merely a single line, but something more as

described in the sutra, following :-

'Rekha' means line; 'kona' means angle; and 'samyavasta'

means the unmanifested state or condition. The single line that is

perceived as the circumference of the circle, is the unmanifested

state of a good number of lines and angles, for the reason that a

circle is reckoned as a polygon of N sides; where the value of N

depends upon the intellectual perception of the observer, and not

upon any other thing.

Two Aspects of the Circle :- We now see two peculiar forms

of the Circle :- 1. A plane figured bounded by one line; and 2. A plane

figure bounded by N lines (A polygon). The one is what is actually

perceived, whereas the other is what is actually superimposed by

the Geometor. In fact, the Space unlimited has neither the shape of

hemisphere, or a circle, nor the shape of a polygon. Unlimited, rather

Infinite Space assumes the shape of the Hemisphere, or a circle,

before the observer, and the observer superimposes infinite lines,

and angles, upon it. From these phenomena of the Space, it is easier

to grasp the various forms of Purnam, the Brahma. Infinite Brahma

presents to the observer the form of Iswara; and the Observer

superimposes infinite numnber of gunas (Anantaguna), upon the

Iswara. The manifestation ofBrahma, as Iswara, is clearly put forth

by the Sruti , thus :- "Upasakanam soukaryartham

Brahmanorupakalpanam". Iswara is the Visible form of Brahma,

just as the circle is the visible form of Space. Anantaguna isthe Superimposition of the observer, after the fashion of the polygon

of N sides. And this Anantaguna is called the Virat Purusha.

Geometrical continuity :- The circle is said to be a polygon of

N sides. By substituting numerical values for N, the law of geometrical

continuity, as observed in the sections of the cone, can as well be

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possibly conceived with certainty, beyond which no decided opinion

can be formed. What is true to the nine numbers, will always prove

true to any number, for the reason that it is only an offspring of Nine

only. What is adopted by the sanscrit Mathematicians as "Na"

the contracted form of Nine, has been copied out as N, byothers.

Conic Sections :- In projective geometry, conic sections are

defined as the projections of a circle; hence, the figures, hyperbola,

parabola and the ellipse, also come under the genus of the Circle.

Thus, we have under the Genus of the Circle the species 1. The line,

2. The angle, 3. the triangle, the square, and similar lateral figures, 4.

The hyberbola, 5. The parabola, and 6. The ellipse. It was observed

by a learned geometer of the 17th century, that 'From the line-pair

we pass through an infinity of hyperbolas to the parabola, and thencethrough an infinity of ellipses, to the Circle." His observations would

have been perfect, had he observed the remaining things as the

species.

The Circle and the Purnam :- Now that we have realised that

the Circle is the Genus of the universe of figures, we can aptly realise

that it stands as a perect representation ofIswara, the Genus of the

Universe at large. It is for the reason that the Circle represents

the Iswara, that it can be the only plane figure, that can stand as the

correct symbol of the Purnam, and none else. Hence the validity of

the sutra "Taddhi Vruttarupam." In fact Purnam cannot find any

tru representation, either in thought, word, or form after the manner

of the space unlimited. It is only through the possibilities, that

Purnam should be realised; and the only possibility is The

Circle.

Parabola and the Ellipse; but it is not sound to say that the Circle is

the Genus of the lateral figures, for the reason that they belong to

entirely different category, the lateral figure, the Genus of which being

the Equilateral Triangle. If the Equilateral Triangle can be proved to

be the effect of the Circle, then the law of geometraical continuity

proves perfect and the Circle would gain the glory of being the

fundamental cause of all the Mathematical figures, bearing

testimony to the Holy Doctrine of the Vedanta, that Purnam

Brahma is the Only cause of the variegated objective World.

The answer to the querry is clearly put forth in the sutras following :-

Sutra 6 :- Vruttat sarvavyavaharavyanjakam Samatribhujam

fi@@6@@ wn|`\N ufi\d+ 6 es eeVs e++ deT uTyT

The word "Sambhutam' is complementary in the sutra, "Vruttat"

means from the Circle; 'Sarvavyavaharavyanjakam" means that

which presents all the forms of usage; "Samatribhujam" means

the equilateral triangle; "Sambhutam" means took its birth; Vruttam

is the visible plane superficies of the Earth, bounded by the horizon.

The forms of geometrical usage are :- the point, the straight line, the

angle, and the lateral figure. The sutra literally means that theequilateral triangle, that presents, all the forms of geometrical

usage, has taken its birth, from the circular plane superficies

of the Earth only. That means that the conception of the Equilateral

triangle is formed out of the circular superficies natural, before the

observer.

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possible for one to think of the circular plane superficies as the

Equitalteral Triangle? The why of the conception and the answer to

the querry is given in the sutra following :-

Sutra 7 :- Adhyasatfi@@7@@ Eo

d+ 7 n


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It has clearly been shown that all the lateral figures have been

developed out of the plane superficies, the Circle; and similar is the

case with the figures, hyperbola, parabola, and the ellipse. Yet it is

maintained by some thinkers and observers that all the lateral figures

are only the result of the evolution of the equilateral triangle, and that

the equilateral triangle is the result of superimposition. How the lateral

figures are the development of the equilateral triangle, is clearly

shown in the sutras following :-

Sutra 9:- Tribhujat Pancha Tanmatrani Tanmatrebhyaha

Pancha Mahatrikonani Tebhyokhilachakrani.

fi @@9@@ ufi\n`YYfium ofiz: `YufiNzmu

ozzDDDDDuQYN umd+ 9 uTC +# HD Hu'

|+#eTVD u\#D 'Tribhujat' means from the equilateral triangle; 'Pancha

Tanmatrani', five forms having the same for as the equilateral

triangle; from the Tanmatras, is the meaning of

Panchatanmatrebhyaha; 'Pancha Mahatrikonani', five great

triangles, "Tebhyaha", from the five great triangles,

'Akhilachakrani' , all the figures, the word 'Sambhutani' whichmeans "have evolved", is complementary in the Sutra.

Five Tanmatras are five equilateral triangles; five Mahatrikonani

are :- 1. the Isoceles, 2. the Scalene, 3. the Right angled, 4. the

Obtuse angled, and 5. the Acute angled; Akhila Chakrani are the other

lateral figures, such as the quadrilaterals, Pentagons, Haxagons, &

How the equilateral triangle, so trivial in nature, gives rise to so

many forms of figures wonderful, is explained by the sutra coming.

Sutra 10 : Udrekat

fi@@10@@ GzNod+ 10


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here in described in brief the second form of the Udreka of the

Equilateral Triangle.

Experiment 1:- Let ABC be an Equilateral triangle. Fig.1

Revolve the straight line C A , about the point C. So as to make anangle CA, equal ot the angle ABC or ACB. The straight line CA, no w

occupies the position CD. Fig.2

1.Join BD, cutting AC, in E; and observe what new features the

figure presents before you. Angle BEC, which is Right; angle BCD,

which is Obtuse; and angle ACB, which is acute. Triangle CBD,

which is Isosceles, triangle BEC, which is Scalene. Triangle BEC,

Which is Right-angled; triangle BED, which is Obtuse angled, and

triangle ABC, which is Acute-angled.

All these things the Geometer obtained by simply drawing the

straight line BD from the Point B to D. Had it not been for this

straight line, he would not have had so much knowledge; as such he

should be more grateful to the straight line joining B & D. So he

gives expression to his gratitude in the postulate which he ranked as

the first; "That a straight line may be drawn from any one point to any

other point."

2. Now Join AD, and you will be surprised to see a beautiful

figure ABCD, (fig.3) a quadrilateral, whose four sides are equal to

one another, but whose angles are not right angles. It is called a

Rhombus.

Experiment 2 :-Fig 4. - in the same figure, revolve CD, in the

same way as to make an angle with the straight line CD, equal to the

angle ABC. Now the straight line CD, occupies the position CF.

1.Now join the point B with F; and you will be astonished to see

that B is nothing but the prolongation of BC to F.

And it is this joining in this deflection of CA, that blessed the

Geometer, with the 2nd Postulate, "That a finite, that is to say, a

terminated straight line may be produced to any length in that straight

line."

2.Join DF, and the new figure formed is the quadrilateral ABFD,

which is a Trapezium.

3. And join A; no new feature is to be observed.

Experiment 3 :-Fig. 4 - Revolve again CF in the same manner

as above. Now you will see that it occupies the position CG.

1. Now join BF & GF and and the figures newly obtained are :-1. the quadrilateral ABGF, which is a rectange (an oblong) and 2.

Pentagon ABGFD.

2.And join DG, no new figure is obtained.

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Experiment 4 :-5 - Revolve again the straight line CG in thesame way as above and it now occupies the position CH.

1. Now join BH & HG; and the new figure obtained is ADFGHB,

which is called a Hexagon.

2. Join AH & HF as well; and no new figure is obtained. Now

you will be surprised to see that in the next deflection or Revolutin

CH (CA) coincides with CB, and in the last and the 6th Revolution or

deflection, the straight line CA occupies its own position; and as such

in the next two revolutions, there is no possibility for further formation

of any figures.

Experiment 5:-Fig 6 - Now trace the course of the revolution

of CA about the point C, by marking the course with dots. The

consequence is the Circle; a circle with the radius CA, and the centre

gratitude in Postulate the third. That a circle may be described

from any centre at any distance from the centre."

A side of the Equilateral Triangle is revolved, and the changes

are observed one after another; as such we observe the development

rather evolution of figures as follows :-

1.Straight lines, 2. Triangles, 3. Quadrilateral, 4. Pentagon, 5.

Hexagon and 6. the Circle and its accompaniments; as well as the

order of the postulates, one after the other. We can as well observe

that all other forms of figures are merely the combinations of the

different kinds of trianges only, which are the result of the evolution

of the Equilateral Triangle. And the Equilateral triangle is the result of

superimposition upon the Circle. Hence the geometrical continuity

is perfect.This Geometrical continuity is neither a conjecture, nor an after

thought, but is supported by the elements of Geometry, with all

accuracy of thought and arrangement; and this harmony is proclaimed

by the sutra, following:-

Sutra 11 : Samanvayat

fi@@11@@ o

d+ 11

deTqjY'Samnvayam' means a lucid investigation and discussion. A

lucid investigation and argument of the logical sequence of the

arrangement of the Elements of Geometry, clearly shows that this

Evolution forms the backbone of the grand work.

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straight lines and triangles. From the 33rd to the 45th, triangles and

parallelograms are discussed. Proposition 46th and the only 14

propositions of Book II, treat of squares and rectangled. Books III

and IV, treat of the Circle and its relation to the other kinds of figures;

and Book IV, nearly closes with the constrution of a regular Hexagon.

So the Geometer commences his work with the construction of an

Equilateral Triangle, and finishes that portion of it, which treats in

general as well as in special of the properties of all the figures which

he obtained in his Evolution, after the same manner and order, and

nearly concludes the work by the construction of a regular Haxagon,

the last rectilineal figure; and as such the last but one of his Evolution.

The Geometer also hints the Hexagon as the last figure but one in

the Evolution, by simply closing the Book IV with the construction ofa Quindecagon, as the last proposition, where in also he places the

Equilteral Triangle once more.

We can boldly say that Plane Geometry is complete by this

time as the stock of the plane figures and their properties are finished

in these four books, for the reason that no new figure is desbribed or

constructed in the other books. Book V is Algebraical; book VI treats

of the Algebraical relations of the figures described in the first four

books only, even then the squence is not missed at all. Books VII, VIII

and IX, are purely Arithmetical; while book X containes an ingenious

treatment of Geometraical irrational quantities. The remaining three

books treat of the figures in space; as such are generally called solid

Geometry.

Lateral figures is nothing but the Evolution of the Equilateral

Triangle.

It is now clearly shown that the world of lateral figures, is the

result of the positive revolutionof the Triangle, as such Udreka may

be considered as mere positive revolution only. To avoid such

misconceptin, the sutra following, clearly puts forth the functions of

the two forms of Udreka:-

Sutra 12 :- Tenopachayapachayau Chakranam

fi@@12@@ ozzYY{ YN m

d+ 12H|#j|#jT #DyT

The word "Sambhavataha" , which means happen, is comple

mentary, in the Sutra. 'Tena' means by Udreka.

'Upachayapachayau' means Evolution and Involution; 'Chakranam'

means to the figures. The sutra means that Evolution and Involution

happen to the figures by Udreka. Postitive revolution tends to the

Evolution, whereas Negative revolution to the Involution of figures.

By Evolution a simple figure develops to a compound figure; and by

Involution, a compound figure will be reduced to a simple figure,

whether it is development or reduction, it is all Udreka; hence it issaid that Udreka tends to the development or reduction of the figures.

It is said that Udreka effects either Evoltuin or Involution in

figures; the Circle is also considered as a figure; hence, one may be

led away to think that Udreka may as well effect the changes of

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y y

fi@@13@@ ouNzm uNzm

d+ 13qT cDd cDd

The word "Udreka" is complementary in the sutra.

'Nishkonasya' means for that which is devoid of angles; reiteration

of the term Nishkonasya is indicative of the closing of the chapter.

The sutra means that Udreka cannot effect the changes of Evolution

or Involution to a figure that is devoid of any angle. It is only the Circle

that is devoid of any kind of angle; hence Udreka has nothing to do

with th Circle or the Ellipse. It is only the figures that contain any kind

of angle, that are subject to the influences of Udreka. Hence any

figure is liable to the changes of Evolution and Involution, when it is

not developed to the status of the Circle. If any figure evolves to the

stae of the Circle, then it remains unchangeable for ever. And this is

what is called the Salvation or Mukti of the figures. Unless and

until the figures achieve that holy stage they are liable to the chances

of Evolution and Involution. And the status of the Circle is above

all the influences of Udreka.

Purnamimamsayam Prathamamahnikam

And thus closes the first day of the Purnamimamsa.

Geometrical figures, without itself undergoing any change

whatever, by the mere Superimposition of the observer; and

that Udreka, Revolution positive or negative, cannot under any

circumstances, exert any kind of changes evolutionary or

involutionary, upon the Circle, for the reason that it is devoid

of any kind of angle. But it is likely that thinkers, often misconceive

and misconstrue the real aspect, and fall a prey to false theories and

doctrines, the type of which, we here put forth in the very words of an

authoritative mathematician :- "We consider space as filled with

points, lines and planes, and these we call the elements out of which

our figures are to be formed, calling any combination of these

elements of "figure". A simple analysis of the above statement, would

sho how queer and confusive it is. Herein it is stated that the points,lines and planes, are the elements, and that any combination of these

elements, is a figure. Thus one is led to conceive that any combination

of points is a figure; or any combination of planes, is figure. From

this a hasty reader may conclude that, 1. the points are the cause of

the figures; 2. the lines are the cause of the figures; and 3. the planes

are the canse of the figures. Thus the cause of the figures cannot

be positively described as some thing or the other, but creates a

dilemma as to which of the three, is the real cause of figures. Even

then it is meaningles. If a point is defined as that which has no parts

or which has no magnitude, then there would be no possibility for

such points to combine for the production of a figure with parts or

magnitude. We know full well that the centre at which thousand radii

meet will remain a point only, and never produce any kind of figure

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y p g ;

statement proves only a meaningles rigmarole and not a crude theory

even. Whatever may be the sanity or insanity of the above theory, it

is likenly that it puts forht three different things as the causes of the

figures : 1. point, 2. line, and 3. plane, which are entirely different

from what is hitherto justified and affirmed. Unless and until the

contradictions are removed, truth cannot be established; hence to

remove all possible contradictions, the second Ahnica is

commenced.

The Ahnica starts with the refutation of the 'Bindukaranavada'

which appears diametrically antagonistic to the fundamental doctrine.

Sutra 1:- Binduritichennayogyatva

fi@@1@@ utuuo YzzSno

d+ 1 _+Y

The word Karanam which means cause, is complementary in

the sutra. Bindu means, Point in Geometry, Cipher in Arithmetic,

and Anuswara in Sanscrit language. A point is defined as that which

has no parts or which has no magnitude, Cipher is two-fold. Absolute

nothing, the negligible infinitesimal. Anuswara is that which is

pronounced along with others, but has no independent status of its

own. Ayogyatva means impotency. The sutra means that if Bindu is

considered to be the cause, it is not, for the reason that it is not

potential. bindu is simply nothing, in whatever aspect it may be

viewed. Nothing can never be the cause of something. Point is

g g

infinitesimal even it is not at all potential to be the cause, proclaims

the sutra folloiwng :-

Sutra 2 :- Anutvachchafi@@2@@ EmnXY

d+ 2 nDT#

Anutva means the property of being infinitely small, similar to

the atom of the scientists. If the point were to be cosidered to have

some magnitude, then it would have some form; what form can be

fixed to it then? The form of a circle, for the reason that it is called

the point-circle. If it were to be a circle, then what is its radius? It is

zero. Then it is all the more to say that it is mere nothing, and nomore. If any magnitude were to be thought of to the point, it would be

confusion worse confounded.

Under any circumstance it is impotent to be the subsratum of

any thing, urges the sutra following:-

Sutra 3:- Adhikaranatvayogachcha

fi@@3@@ EuNmnzTXY

d+ 3

n~sDj>#Adhikaranatva means the capacity to be the substratum.

There cannot be a superimposition, without something or other as

the substratum. Point is nothing; hence nothing can be superimposed

upon it.

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of the Nayyayikas, and the Sunyavada of the Saugatss, are as well

refuted.

Seeing the circle as the final object in the Evolution of the

Equilateral Triangle, one may be led to conclude that the Triangle is

the fundamental cause; to avoid such misconception, the following

sutra proceeds :-

Sutra 4 :- Trikonamitichennasambhavat

fi@@4@@ ufiNzmuuo Yzo

d+ 4 D$T#H d+uyY

In the sutra, the word Karanam is complementary. Trikona,means triangle; Asmbhava means out of existence, that is

impossible. The Sutra means that if the triangle be considered as

the cause, it is not, for the reason that it has no real existence at all.

The argument for the unreality of the triange is advanced by the

sutra coming :-

Sutra 5 :- Sasavishanavt Rujurekha

fi@@5@@ umtw\zQd+ 5 XX$cDe


82/120

p y

Sastradayaha means Sruti,Smruti, Reason and Direct Perception.

The reiteration of the term is indicative of the closing of the Ahnica.

The highest authorities of Knowledge are the Struti and Smruti etc.

With reference to the straight line; we have before us the

testimony of the mathematicians, thus :-

"These notions (the simplest line - the straight line, the simplest

surface) we possess, but to difine them accurately, is difficult. The

Definition "A straight l ine is that which lies evenly between its extreme

points" must be meaningless to any one who has not the notion of

straightness in his mind. Neither does it state a property of the straight

line which can be used in any further investigation."

"By a line we mean a straight line in its entirety, extending both

ways to infinity."

"Parallel straight lines are such as are in the same plane, ever

so far being produced both ways do not meet."

"Parallel lines are lines which meet at infinity."

"Lines which meet at infinity are called parallel."

In the confocal system, the straight line is called the Line ellipse.

These notions of the Geometers are in themselves, unsound,

and unprincipled. It is only the illustration adopted by the Vedantic

Geometers that can be the specific illustration to place before the

observers, the ideas of a straight line, an equilateral triangle, and

their relation to the Circle. The vedantic Geometers who aimed at a

picture ofPrakruti, which is defined as Trigunatmika, caught hold of

present an Inscribed equilateral triangle, wherein the strings

represent the three straight lines nay, the sides of the triangle, and

the bows, the Circle. The Circle is ever present in nature as the

Horizon, whereas the Equilateral Triangle is the production of the

Human intellect. Hence the Triangle has no positive existence, and

so is the case with a straight line. Hence the triangle cannot under

any circumstances have the potency to be the cause fundamental.

By the refutation of the Trikonakaranavada, the

Prakrutikaranavada of the Sankhyas and Yogis, and the similar

theories of others have been entirely refuted.

Purnamimamsayam Dwitiyam Ahnicam

Thus closes the second day of Purnamimamsa.

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g p

possible graphical representation of the Purnam, Brahma. The

grandeur of the Circle can be fully realised beyond doubt, from a

knowledge of the Vedantic significance of the other figures, as well.

hence the third Ahnica proceeds with the exposition of the Vedantic

conceptions represented by the prominent figures for the guidance

of the aspirants.

The Circle is said to be the possible representation of the

Purnam; as such the real nature of the Purnam, cannot be perfectly

comprehended from the Circle itself, without any guidance. So the

first two Sutras are introduced to define the real nature of the Purnam,

The definition ofPurnam, "Yachachakranamadhishtanam" given

in Ahnica I, is only a secondary one; whereas the definition givenhere, is primary.

Sutra 1 : Niravayavam Nirgunam Nishkriyam

Chinmatram Purnam

fi@@1@@ u uT|m uuN uYfi m|

d+ 1 sejTe+ sTZD+ wjT+ H+ |PsyT

A 'Niravayavam' means devoid of limbs (lines); 'nirgunam',

devoid of qualities (angles); 'nishkriyam', devoid of any action

(Udreka); 'Chinmatram', pure Intelligence only' 'Purnam' All-pervading.

The sutra means that the All-pervading Purnam, Brahma, is devoid

of any limbs or qualities, or actions; but it is Pure Intelligence,

Supreme.

y g p ,

Anantasaktimat. So the sutra appears to be fallacious. No. A little

more observation of the nature of the circumference, would place

the observer on a higher plane, and the truth of the sutra can be

realised to the very letter. What is the circumference, then? It is theHorizon bounding Earth and Skies. The horizon is said to be an

immaginary line; as such it has no positive existence whatever.

Weakness of the vision of sight has given birth to the immaginary

curved line, and further weakness of intellect, rather ignorance has

led to the misconception of lines and angles, in multifarious ways. In

fact all these conceptions are the result of the short-minded nature

of the observer and there is not an iota of any line or angle in the

horizon. Hence it can be maintained with all rhyme and reason that

the space is beyond all limitations; as such Purnam is all the more

above all limitations of avayava (limb). Hence Purnam is

Niravayavam; hence nirgunam; hence nishkriyam. in order that

the Purnam may not be misconstrued as the space unlimied, it is

described as Chinmatram - Supreme Intelligence.

Now that the Purnam is defined as Intelligence, one will naturally

be led away to think of the multitude ofPurnams, after the fashion of

the Sankhyas or the yogis or similar schooolmen. To warn such

misconceptions, the sutra following proceeds :-

Sutra 2 :- Ekamevadwitiyamfi@@2@@ LNzuoy

d+ 2 @yTy~rjT+

'Ekam' means One; 'Eva' only; 'Adwitiyam', without a second.

The stura means that Purnam is one only without a second. Every

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variety of the tree from other trees. Vijatiya variety is that which is

observed in the object of a different species; that is the variety of the

tree from the stone and etc. The sutra refutes the three-fold variety

with reference to the Purnam, through the three words respectively.This can be well established from a close observation of the Circle.

Every observer feels the existence of one and only one superficies

without a second, whatever may the relative conception of the centre

be. He observes not any variety in the plane superficies itself, nor

observes any other superficies of a similar type, or any other thing

widely different from the supreficies. Hence it can be argued and

realised that Purnam is One and only One, without a second.

The real status of the Purnam being justified from the holy

graphic representation of the superficies, the Circle; the next sutradescribes the real aspect of the imaginary line, the horizon:-

Sutra 3:- Paridhiravaranam

fi@@3@@ uum

d+ 3 |]~sesD+

'Paridhihi' means the circumferecne; 'Avaranam' is that form

of force ofAvidya, or Maya, that makes the original nature of the

Purnam shut up from the ordinary course of observation. It is clear

own Self, and makes him feel that he is some s

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