आर्यभटीय – आर्यभट- Arya Vhatiya by Arya Vat-[400-350 BCE]

Contents 

  1. Gitikapada: (13 verses)

  2. Ganitapada (33 verses)

  3. Kalakriyapada (25 verses)

  4. Kalakriyapada (25 verses)

दश-गीतिका-पाद 

१.१ ॰प्रणिपत्य एकमनेकं कं सत्यां देवतां परं ब्रह्म्

१.१ आर्यभटस्त्रीणि ॰गदति गणितं काल-क्रियां गोलम्

प्रणिपत्य एकमनेकं कं सत्यां देवतां परं ब्रह्म ।
आर्यभटः त्रीणि गदति गणितं कालक्रियां गोलम् ॥ १ ॥

अस्याः पदविभागः: – प्रणिपत्य, एकम्, अनेकम्, कम्, सत्याम्, देवताम्, परम्, ब्रह्म, आर्यभटः, त्रीणि, गदति, गणितम्, कालक्रियाम्, गोलम् । [भास्कर-विरचित-भाष्य]

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आपस्तम्ब शुल्बसूत्रम् – Apastambha Sulva Sutram-1000 BCE

आपस्तम्ब शुल्बसूत्रंम्

विहारयोगान्व्याख्यास्यामः ॥ १.१ ॥

यावदायामं प्रमाणं ॥ १.२क ॥

तदर्धमभ्यस्यापरस्मिंस्तृतीये षड्भागोने लक्षणं करोति ॥ १.२ख ॥
पृष्ठ्यान्तयोरन्तौ नियम्य लक्षणेन दक्षिणापायम्य निमितं करोति ॥ १.२ग ॥
एवमुत्तरतो विपर्यस्येतरतः स समाधिः ॥ १.२घ ॥
तन्निमित्तो निर्ह्रासो विवृद्धिर्वा ॥ १.२च ॥

आयामं वाभ्यस्यागन्तुचतुर्थं आयामश्चाक्ष्णया रज्जुस्तिर्यङ्भानीशेषः । व्याख्यातं विहरणं ॥ १.३क ॥
दीर्घस्याक्ष्णयारज्जुः पार्श्वमानी तिर्यङ्मानी च यत्पृथग्भुते कुरुतस्तदुभयं करोति ॥ १.४क ॥
ताभिर्ज्ञेयाभिरुक्तं विहरणं ॥ १.४ख ॥
चतुरश्रस्याक्ष्णयारज्जुर्द्विस्तवतीं भूमिं करोति । समस्य द्विकरणी ॥ १.५ ॥
प्रमाणं तृतीयेन वर्धयेत्तच्चतुर्थेनात्मचतुस्त्रिंशोनेन सविशेषः ॥ १.६ ॥

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Vedic measure of distance: Yojana-योजन

1 yojana is equivalent to 14.484096 km = 9 miles

1000 dhanus =1 yojana

1 dhanu = 96 angulas = 4 hastas

1 angula = ¾ inch=10 Yava

1 yojana=4 Krosas= 4000 Hastas=8000 feet

1 Gavyūti (गव्यूति-2.01km)=2000 Dhanus

Speed Of Light = 2202 Yojanas/Nimishardha or 19818 Miles/0.106 Second

तथा च स्मर्यते…

योजनानां सहस्रे द्वे द्वे शते द्वे च योजने।
एकेन निमिषार्धेन क्रममाण नमोस्तु ते॥

[Mandal 1, Sukta 50, Mantra 4, Sayanacharya Commentary]


30 Muhurtas/60 Nadis = 24 hours (अहोरात्रम्)

1 Muhurta=48 Minutes=30 Kalas= 2 Nadis

1 Kala=96 Second=30 Kashtas

1 Kastha=3.2 Second=15 Nimishas

1 Nimishas=0.213 Second

1/2 Nimishas=0.1063 Second


 

Drake Equation

For the existence of extraterrestrial civilizations

N = R* x fp x ne x fl x fi x fc x L

Where:

N = The number of civilizations in the Milky Way Galaxy whose electromagnetic emissions are detectable.

R* = The rate of formation of stars suitable for the development of intelligent life.

fp = The fraction of those stars with planetary systems.

ne = The number of planets, per solar system, with an environment suitable for life.

fl = The fraction of suitable planets on which life actually appears.

fi = The fraction of life bearing planets on which intelligent life emerges.

fc = The fraction of civilizations that develop a technology that releases detectable signs of their existence into space.

L = The length of time such civilizations release detectable signals into space.

There are an estimated 200 – 400 billion stars exist within our Milky Way, and modern estimates say that there between 1.65 ± 0.19 and 3 new star form every year.

Arithmetic

Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics

It is the method known as the “Method of the Indians” or in Latin “Modus Indoram” that has become our arithmetic today. Prior to this, basic arithmetic operations were highly complicated affairs. Seventh century Syriac Bishop Severus Sebhokt mentioned this method and stated that the method of the Indians is beyond description. Indian arithmetic was much simpler than the Greek arithmetic simply due to the simplicity of the Indian number system which had a zero and place value notation. Arabs learned this new method and called it “Hesab” or “Hindu Science”. Fibonacci or Leonardo of Pisa is one of the first European mathematicians who introduced the “Method of the Indians” to Europe. In his famous book “Liber Abaci” Fibonacci says that compared to this new method all other methods were mistakes.

Decimal arithmetic

Decimal notation constructs all real numbers from the basic digits, the first ten non-negative integers 0,1,2,…,9. A decimal numeral consists of a sequence of these basic digits, with the “denomination” of each digit depending on its position with respect to the decimal point: for example, 507.36 denotes 5 hundreds (102), plus 0 tens (101), plus 7 units (100), plus 3 tenths (10-1) plus 6 hundredths (10-2). An essential part of this notation (and a major stumbling block in achieving it) was conceiving of 0 as a number comparable to the other basic digits.

Algorism comprises all of the rules of performing arithmetic computations using a decimal system for representing numbers in which numbers written using ten symbols having the values 0 through 9 are combined using a place-value system (positional notation), where each symbol has ten times the weight of the one to its right. This notation allows the addition of arbitrary numbers by adding the digits in each place, which is accomplished with a 10 x 10 addition table. (A sum of digits which exceeds 9 must have its 10-digit carried to the next place leftward.) One can make a similar algorithm for multiplying arbitrary numbers because the set of denominations {…,102,10,1,10-1,…} is closed under multiplication. Subtraction and division are achieved by similar, though more complicated algorithms.

Arithmetic operations

The traditional arithmetic operations are addition, subtraction, multiplication and division, although more advanced operations (such as manipulations of percentages, square root, exponentiation, and logarithmic functions) are also sometimes included in this subject. Arithmetic is performed according to an order of operations. Any set of objects upon which all four operations of arithmetic can be performed (except division by zero), and wherein these four operations obey the usual laws, is called a field.

Number theory

The term arithmetic is also used to refer to number theory. This includes the properties of integers related to primality, divisibility, and the solution of equations by integers, as well as modern research which is an outgrowth of this study. It is in this context that one runs across the fundamental theorem of arithmetic and arithmetic functions.

Topics

» Ackermann function » Addition » Additive inverse
» Anomalous cancellation » Arithmetic » Arithmetic precision
» Arithmetic rope » Casting out nines » Computer arithmetic
» Division (mathematics) » Division algorithm » Elementary arithmetic
» Empty product » Empty sum » Factorization
» Finite field arithmetic » Fractions » Galley division
» Hyper operator » Lecnac » List of basic arithmetic topics
» Location arithmetic » Multiple (mathematics) » Multiplication
» Peano axioms » Presburger arithmetic » Promptuary
» Rabdology » Rounding » Shabakh
» Significant figures » Subtraction » Subtraction without borrowing
» Successor function » Sudan function » Summation
» Swami Bharati Krishna Tirtha’s Vedic mathematics » Tetration » Trachtenberg system
» Two plus two make five

More Arithmetic topics

 Arithmetic mean  Arithmetic  Presburger arithmetic
 Ordinal arithmetic  Arithmetic lattice  Arithmetic group
 Elementary arithmetic  Philosophy of Arithmetic  Arithmetic-geometric mean
 Arithmetic rope  Affine arithmetic  Non-standard arithmetic
 Arithmetic progression  Arithmetic shift  Arithmetic (song)
 Arithmetic coding  Arithmetic precision  Arithmetic function
 Arithmetic genus  Arithmetic underflow  Arithmetic overflow
 Treviso Arithmetic  The Devil’s Arithmetic  Verbal arithmetic
 Quasi-arithmetic mean  Location arithmetic  Roman arithmetic
 Robinson arithmetic  Introduction to Arithmetic  Saturation arithmetic
 Second-order arithmetic  Heyting arithmetic  Significance arithmetic
 Modular arithmetic  Linear Arithmetic synthesis  Primitive recursive arithmetic
 Reading, Writing, and Arithmetic  Emotional Arithmetic (film)  Fundamental theorem of arithmetic
 Fixed-point arithmetic  Finite field arithmetic  Arbitrary-precision arithmetic
 Arithmetic logic unit  Arithmetic of abelian varieties  Infinite arithmetic series
 Generalized arithmetic progression  Hilbert’s arithmetic of ends  Serial Number Arithmetic

Multiplication table

× 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120
7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140
8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160
9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180
10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220
12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240
13 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 247 260
14 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252 266 280
15 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300
16 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320
17 17 34 51 68 85 102 119 136 143 170 187 204 221 238 255 272 289 306 323 340
18 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360
19 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 361 380
20 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400


 

Algebra-Bij ganitam

Algebra is a branch of mathematics connected with the study of structure, relation, and quantity.

The origin of Bij-ganitam is ancient India. Persian first learn it from here and then from them the Greeks. The Algebra name is derived from the treatise written by the Persian mathematician Muhammad bin Mūsā al-Khwārizmī  820CE, titled (in Arabic كتاب الجبر والمقابلة )Al-Kitab al-Jabr wa-l-Muqabala (meaning “The Compendious Book on Calculation by Completion and Balancing”)

Major fields of mathematics :

Logic • Set theory • Algebra (Abstract algebra – Linear algebra) • Discrete mathematics • Combinatorics • Number theory • Analysis • Geometry • Topology • Applied mathematics • Probability • Statistics • Mathematical physics • Ring (mathematics) and Field (mathematics)

Elementary and Abstract Algebra

Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. Although in arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur, in algebra, numbers are often denoted by symbols (such as a, x, y).

Abstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts.

The word algebra is also used for various algebraic structures:

Algebra over a field
Algebra over a set
Boolean algebra
F-algebra and F-coalgebra in category theory
Sigma-algebra


Fields of algebra

» Abstract algebra » Affine Hecke algebra » Algebra
» Algebra homomorphism » Algebra stubs » Algebraic element
» Algebraic extension » Algebraic function » Algebraic geometry
» Algebraic number » Algebraic solution » Algebraic topology
» Alternatization » Anyonic Lie algebra » Associative algebra
» Automorphism » Binary operation » Binomial
» Binomial theorem » Brahmagupta-Fibonacci identity » Canonical form
» Category theory » Closed-form expression » Coefficient
» Combinatorics » Completing the square » Computer algebra
» Congruence relation » Conjugate (algebra) » Consequence operator
» Cuntz algebra » Cycle (mathematics) » Degree (mathematics)
» Derivative (generalizations) » Determinant » Digital root
» Dimension » Distributive homomorphism » Distributive lattice
» Elementary algebra » Expression (mathematics) » Factorization
» Filtration (mathematics) » Galois theory » Generalized arithmetic progression
» Goursat’s lemma » Hall polynomial » Hecke algebra
» Homological algebra » Identity element » Immanant of a matrix
» Indeterminate (variable) » Intersection (set theory) » Inverse element
» Irreducible polynomial » Isomorphism » Iterated binary operation
» K-theory » K-theory (physics) » Kernel (algebra)
» Kernel (set theory) » Lattice (order) » Laws of Form
» List of basic algebra topics » Mathematical identities » Monomial
» Monomial basis » Multinomial theorem » Multiplicative inverse
» Nested radical » Operand » Operation theory
» Operator » Order of operations » Pairing
» Partial fraction » Partial fraction decomposition » Perfect square
» Permanent » Permutations » Plugging in (algebra)
» Polynomials » Power set » Ratio
» Rational root theorem » Recurrence relation » Relation algebra
» Ring theory » Square (algebra) » Sylvester’s determinant theorem
» Symbolic method » Symmetric difference » Symmetric functions
» System of linear equations » Temperley-Lieb algebra » Theory of equations
» Topological module » Transforming polynomials » Trinomial
» Union (set theory) » Unital » Universal algebra
» Variable » Variety (universal algebra)


 More  on Algebra

Derivative algebra (abstract algebra) Map algebra F-algebra
The Algebra of Ice C-algebra *-algebra
MV-algebra Algebra Pre-algebra
Max-plus algebra Rng (algebra) B
-algebra
En (Lie algebra) Lie algebra Abstract algebra
Steenrod algebra Derivative algebra Hopf algebra
Multilinear algebra Group algebra Elements of Algebra
Hecke algebra Modular Lie algebra Graded algebra
De Morgan algebra Heyting algebra Plugging in (algebra)
Graded Lie algebra Elementary algebra Jordan algebra
Monster Lie algebra Linear algebra Operator algebra
Relation algebra Poisson algebra Free Lie algebra
Example of a non-associative algebra Characteristic (algebra) Magma (algebra)
Quaternion algebra Exterior algebra Cuntz algebra
Spectrum of a C*-algebra Strip algebra Topological algebra
Cube (algebra) Matrix algebra Enveloping algebra


Chronology  of key algebraic developments :

Circa 2800 BC: Bodhayan Collected old Theories and compiled in Sulva Sutram [India].  It explained so-called Pythagorean triples algebraically, finds geometric solutions of linear equations and quadratic equations of the forms ax2 = c and ax2 + bx = c, and finds two sets of positive integral solutions to a set of simultaneous Diophantine equations.

Circa 1800 BC: The Old Babylonian Strassburg tablet seeks the solution of a quadratic elliptic equation.
Circa 1600 BC: The Plimpton 322 tablet gives a table of Pythagorean triples in Babylonian Cuneiform script.
Circa 600 BC: Indian mathematician Apastamba, in his Apastamba Sulba Sutra, solves the general linear equation and uses simultaneous Diophantine equations with up to five unknowns.
Circa 300 BC: In Book II of his Elements, Euclid gives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots. The construction is due to the Pythagorean School of geometry.
Circa 300 BC: A geometric construction for the solution of the cubic is sought (doubling the cube problem). It is now well known that the general cubic has no such solution using Euclidean tools.
Circa 100 BC: Algebraic equations are treated in the Chinese mathematics book Jiuzhang suanshu (The Nine Chapters on the Mathematical Art), which contains solutions of linear equations solved using the rule of double false position, geometric solutions of quadratic equations, and the solutions of matrices equivalent to the modern method, to solve systems of simultaneous linear equations.
Circa 100 BC: The Bakhshali Manuscript written in ancient India uses a form of algebraic notation using letters of the alphabet and other signs, and contains cubic and quartic equations, algebraic solutions of linear equations with up to five unknowns, the general algebraic formula for the quadratic equation, and solutions of indeterminate quadratic equations and simultaneous equations.
Circa 150 AD: Hellenized Egyptian mathematician Hero of Alexandria, treats algebraic equations in three volumes of mathematics.
Circa 200: Hellenized Babylonian mathematician Diophantus, who lived in Egypt and is often considered the “father of algebra”, writes his famous Arithmetica, a work featuring solutions of algebraic equations and on the theory of numbers.
499: Indian mathematician Aryabhata, in his treatise Aryabhatiya, obtains whole-number solutions to linear equations by a method equivalent to the modern one, describes the general integral solution of the indeterminate linear equation and gives integral solutions of simultaneous indeterminate linear equations.
Circa 625: Chinese mathematician Wang Xiaotong finds numerical solutions of cubic equations.
628: Indian mathematician Brahmagupta, in his treatise Brahma Sputa Siddhanta, invents the chakravala method of solving indeterminate quadratic equations, including Pell’s equation, and gives rules for solving linear and quadratic equations.
820: The word algebra is derived from operations described in the treatise written by the Persian mathematician Muḥammad ibn Mūsā al-Ḵwārizmī titled Al-Kitab al-Jabr wa-l-Muqabala (meaning “The Compendious Book on Calculation by Completion and Balancing”) on the systematic solution of linear and quadratic equations. Al-Khwarizmi is often considered as the “father of algebra”, much of whose works on reduction was included in the book and added to many methods we have in algebra now.
Circa 850: Persian mathematician al-Mahani conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra.
Circa 850: Indian mathematician Mahavira solves various quadratic, cubic, quartic, quintic and higher-order equations, as well as indeterminate quadratic, cubic and higher-order equations.
Circa 990: Persian Abu Bakr al-Karaji, in his treatise al-Fakhri, further develops algebra by extending Al-Khwarizmi’s methodology to incorporate integral powers and integral roots of unknown quantities. He replaces geometrical operations of algebra with modern arithmetical operations, and defines the monomials x, x2, x3, … and 1/x, 1/x2, 1/x3, … and gives rules for the products of any two of these.
Circa 1050: Chinese mathematician Jia Xian finds numerical solutions of polynomial equations.
1072: Persian mathematician Omar Khayyam develops algebraic geometry and, in the Treatise on Demonstration of Problems of Algebra, gives a complete classification of cubic equations with general geometric solutions found by means of intersecting conic sections.
1114: Indian mathematician Bhaskara, in his Bijaganita (Algebra), recognizes that a positive number has both a positive and negative square root, and solves various cubic, quartic and higher-order polynomial equations, as well as the general quadratic indeterminant equation.
1202: Algebra is introduced to Europe largely through the work of Leonardo Fibonacci of Pisa in his work Liber Abaci.
Circa 1300: Chinese mathematician Zhu Shijie deals with polynomial algebra, solves quadratic equations, simultaneous equations and equations with up to four unknowns, and numerically solves some quartic, quintic and higher-order polynomial equations.
Circa 1400: Indian mathematician Madhava of Sangamagramma finds iterative methods for approximate solution of non-linear equations.
1535: Nicolo Fontana Tartaglia and others mathematicians in Italy independently solved the general cubic equation.
1545: Girolamo Cardano publishes Ars magna -The great art which gives Fontana’s solution to the general quartic equation.
1572: Rafael Bombelli recognizes the complex roots of the cubic and improves current notation.
1591: Francois Viete develops improved symbolic notation for various powers of an unknown and uses vowels for unknowns and consonants for constants in In artem analyticam isagoge.
1631: Thomas Harriot in a posthumus publication uses exponential notation and is the first to use symbols to indicate “less than” and “greater than”.
1682: Gottfried Wilhelm Leibniz develops his notion of symbolic manipulation with formal rules which he calls characteristica generalis.
1680s: Japanese mathematician Kowa Seki, in his Method of solving the dissimulated problems, discovers the determinant, and Bernoulli numbers.
1750: Gabriel Cramer, in his treatise Introduction to the analysis of algebraic curves, states Cramer’s rule and studies algebraic curves, matrices and determinants.
1824: Niels Henrik Abel proved that the general quintic equation is insoluble by radicals.
1832: Galois theory is developed by Évariste Galois in his work on abstract algebra.


 

तुलाविधिः – Tula-bidhi

सर्षपस्य चतुर्थांशोऽणुः
चतुःसर्षपैर्माषः
चतुर्माषैर्वल्लः
चतुर्वल्लैः सुवर्णैः कर्षः
चतुःकर्षैः पलम्
चतुः पलैः कुडवः
चतुःकुडवैः प्रस्थः
चतुःप्रस्थैराढकः
चतुर्भिराढकैर्द्रोणः १


Anu-Drona

हारीतसंहिता

कालसंख्या – Kala Samkhya

कालसंख्या समासेन परार्द्धद्वयकल्पिता । स एव स्यात् परः कालः तदन्ते प्रतिसृज्यते ।। ५.२

निजेन तस्य मानेन चातुर्वर्षशतं स्मृतम् ।
तत् परार्द्धं तदर्द्धं वा परार्द्धमभिदीयते ।। ५.३

काष्ठा पञ्चदश ख्याता निमेषा द्विजसत्तमाः ।
काष्ठास्त्रिंशत्‌ कला त्रिंशत् कला मौहूर्त्तिकी गतिः ।। ५.४

तावत्‌संख्यैरहोरात्रं मुहूर्त्तैर्मानुषं स्मृतम् ।
अहोरात्राणि तावन्ति मासः पक्षद्वयात्मकः ।। ५.५

तैः षड्‌भिरयनं वर्षं द्वेऽयने दक्षिणोत्तरे ।
अयनं दक्षिणं रात्रिर्देवानामुत्तरं दिनम् ।। ५.६

दिव्यैर्वर्षसहस्त्रैस्तु कृत त्रेतादि संज्ञितम् ।
चतुर्युगं द्वादशभिः तद्विभागं निबोधत ।। ५.७

चत्वार्याहुः सहस्त्राणि वर्षाणां तत्कृतं युगम् ।
तस्य तावच्छती सन्ध्या सन्ध्यांशश्च कृतस्य तु ।। ५.८

त्रिशती द्विशती सन्ध्या तथा चैकशती क्रमात् ।
अंशकं षट्‌शतं तस्मात् कृसन्ध्यांशकै विना ।। ५.९

त्रिद्व्येकसाहस्त्रमितो विना सन्ध्यांशकेन तु ।
त्रेताद्वापरतिष्याणां कालज्ञाने प्रकीर्त्तितम् ।। ५.१०

एतद् द्वादशसाहस्त्रं साधिकं परिकल्पितम् ।
तदेकसप्ततिगुणं मनोरन्तरमुच्यते ।। ५.११

ब्रह्मणो दिवसे विप्रा मनवः स्युश्चतुर्द्दश ।
स्वायंभुवादयः सर्वे ततः सावर्णिकादयः ।। ५.१२

तैरियं पृथिवी सर्वा सप्तद्वीपा सपर्वता ।
पूर्णं युगसहस्त्रं वै परिपाल्या नरेश्वरैः ।। ५.१३

मन्वन्तरेण चैकेन सर्वाण्येवान्तराणि वै ।
व्याख्यातानि न संदेहः कल्पि कल्पे न चैव हि ।। ५.१४

ब्राह्ममेकमहः कल्पस्तावती रात्रिरिष्यते ।
चतुर्युगसहस्त्रं तु कल्पमाहुर्मनीषिणः ।। ५.१५

त्रीणि कल्पशतानि स्युः तथा षष्टिर्द्विजोत्तमाः ।
ब्रह्मणः कथितं वर्षं परार्द्धं तच्छतं विदुः ।। ५.१६

तस्यान्ते सर्वसत्त्वानां सहेतौ प्रकृतौ लयः ।
तेनायं प्रोच्यते सद्भिः प्राकृतः प्रतिसंचरः ।। ५.१७

ब्रह्मनारायणेशानां त्रयाणां प्रकृतौ लयः ।
प्रोच्यते कालयोगेन पुनरेव च संभवः ।। ५.१८

एवं ब्रह्मा च भूतानि वासुदेवोऽपि शंकरः ।
कालेनैव तु सृज्यन्ते स एव ग्रसते पुनः ।। ५.१९

अनादिरेष भगवान् कालोऽनन्तोऽजरोऽमरः ।
सर्वगत्वात् स्वतन्त्रत्वात् सर्वात्मत्वान्महेश्वरः ।। ५.२०

ब्रह्माणो बहवो रुद्रा ह्यन्ये नारायणादयः ।
एको हि भगवानीशः कालः कविरिति श्रुति ।। ५.२१

एकमत्र व्यतीतं तु परार्द्धं ब्रह्मणो द्विजाः ।
सांप्रतं वर्त्तते त्वर्द्धं तस्य कल्पोऽयमग्रतः ।। ५.२२

योऽतीतः सोऽन्तिमः कल्पः पाद्म इत्युच्यते बुधैः ।


श्रीकूर्मपुराणे पूर्वविभागे पञ्चमोऽध्यायः