In the history of Indian astronomy and mathematics, the contribution of Aryabhatta I is something unique. He could put forward variety of new hypothesis accurately with the supporting mathematical calculations and evidences. He was borne in 476 AD and wrote his book Aryabhteeya in 499 AD at the age of 23. It is also mentioned that he has written another book known as Suryaasiddhantaprakasa. A commentary for the book on suryasiddhanta.
He starts the text with invocations to the divine powers and to all the planets. The Aryabhateeya alphabetical systems for writing numbers, revolution – numbers and zero point of planets, kalpa and beginning of kali era, planetary orbits, Earth’s rotation, liner diameters, obliquity of the ecliptic and inclinations of orbits, ascending nodes and apogees, manda and sighra epicycles, Rsine differences, and the aim of the dasagitika sutra, mentioned above are given in the first chapter of Aryabhateeya known as gitika section.
introduction, the first ten notational places square and squaring, cube and cubing, square root, cube root determination, areas of a triangle, volume of right pyramids, area of a circle, volume of sphere ( this fromulae is wrong) area of trapezium and plane figures, chord of one sixth of circles, circumference- diameter relation, computation of Rsine table geometrical derivation of Rsine – differences, construction of circles, etc and testing of level and verticality, Radius of the shadow sphere, gnomonic shadow due to lamp post, tip of the gnomonic shadow from the lamp post and height of the latter, theorems of the square of hypotenuse and on square of half chord, arrows of intercepted arcs of interesting circles, sum of the series of an arithmetic progression, number of terms in a series in AP, sum of variety of arithmetical and geometric progressions, product of factors from their sums and squares, quantities from their difference and product, interest on principal- rule of three, simplification of quotients or fractions, reduction of two fractions to a common denominator, method inversion, unknown quantities from sums of all but one, unknown quantities from equal sums, meeting of two moving bodies, pulveriser residual pulverizes, non residual pulverisor are given in the second part.
The third part known as kalakriya or the reckoning of time, the division of time, and circular divisions are given followed by conjunctions of two planets in a yuga, vyatipatas in a yuga, anomalistic and synodic revolutions, jovian years in a yuga, solar years and lunar, civil and sidereal days, intercalary months and omitted lunar days, days of men, manes and god and of Brahma, utsarpini, apasarpini, susamaa and dussama and date of Aryabhata are given as the first part. Then, beginning of the yuga, year and month and day, equality of the linear motion of the planets, consequences of equal linear motion of the planets, non equality of the linear measures of the circular division, relative positions of asterisms and planets, lords of the hours and days, motion of the planets explained through eccentric circles, motion of epicycles, addition and subtraction of mandaphala and sighraphala, a special precorrection for the superior planets, procedure of mandapahala and sighraphala correction for the superior planets and inferior planets are given separately with the distance and velocity of the planets.
In the fourth chapter, namely gola the celestial spheres are explained. The position of ecliptic, motion of the nodes, the Sun and the earth’s shadow, motion of the Moon and the planets, visibility of the planets, bright and dark sides of the earth and the planets, situation of the earth, its constitution and shape, earth compared with kadamba flower, increase and decrease in the size of the earth, apparent motion of the starts due to the earth’s rotation, description of the meru mountain, the meru and the badavamukha, the four cardinal cities, positions of lanka and ujjayini, visible and invisible portions of the bhagola, motion of the bhagola from the north and south poles, visibility of the Sun to the gods, manes and men.
The prime vertical, meridian and horizon, equatorial horizon, the observer in the khagola, the observer’s drnmandala and drkksheparvrutta, the automatic sphere known as globe or golayantra, the latitude triangle, radius of the day circle, the right ascension of Aries, Taurus and Gemini, earthsine, rising of the four quadrants and the individual signs, Rsine of the altitude sankvagra, Sun’s agra, Rsine of the Sun’s prime vertical altitude, Sun’s greatest gnomon and the shadow thereof, the parallax in solar eclipse, Rsine of the zenith distance of the central ecliptic point, drggatijyas of the Sun and the Moon, parallax of the Sun and the Moon, the visibility correction for akshadrkkarma for the Moon, and that of ayanadrkkarma of the Moon, eclipses of the Moon and the Sun, constitution of the Moon, Sun earth and shadow, and the eclipsers of the Sun and the Moon, occurrence of an eclipse, length of the shadow, earth’s shadow at the Moon’s distance, half duration of a lunar eclipse, half duration of the totality of the lunar eclipse, the part of the Moon not eclipsed, measure of the eclipse at the given time, akshavalana, ayanavalana for the first contact, colour of the Moon during eclipse, conditions when the Sun’s eclipse is not to be predicted, planets determined from observations, acknowledgement to Brahma and the conclusions are given as the last part of Aryabhateeya.
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