### ARYABHATIYA ENGLISH TRANSLATION PDF

Note that relevant formatting guidelines may have already been established. Please check this Index’s discussion page. Imbox Aryabhatiya of Aryabhata, English In Kern published at Leiden a text called the Āryabhatīya which claims to be the work. “warrior,” and bhatta means “learned man,” “scholar.” Āryabhatta is the spelling which would naturally be expected. However, all the metrical.

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For his explicit mention of the relativity of motion, he also qualifies as a major early physicist.

While there is a tendency to misspell his name as “Aryabhatta” by analogy with other names having the ” bhatta ” suffix, his name is properly spelled Aryabhata: Aryabhata mentions in the Aryabhatiya that it was composed 3, years into the Kali Yugawhen he was 23 years old.

This corresponds to CE, and implies that he was born in Similarly, the fact that several commentaries on the Aryabhatiya have come from Kerala has been used to suggest that it was Aryabhata’s main place of life and activity; however, many commentaries have come from outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.

Chandra Hari has argued for the Kerala hypothesis on the basis of astronomical evidence. Aryabhata mentions “Lanka” on several occasions in the Aryabhatiyabut his “Lanka” is an abstraction, standing for a point on the equator at the same longitude as his Ujjayini. It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time. Aryabhata is the author of several treatises on mathematics and astronomysome of which are lost.

His major work, Aryabhatiyaa compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times.

## The Aryabhatiya of Aryabhata

The mathematical part of the Aryabhatiya covers arithmeticalgebra tranzlation, plane trigonometryand spherical trigonometry. It also contains continued fractionsquadratic equationssums-of-power series, and a table of sines.

The Arya-siddhantaa lost work on astronomical computations, is known through the writings of Aryabhata’s contemporary, Varahamihiraand later mathematicians and aryabhatiyya, including Brahmagupta and Bhaskara I. This work appears to be based on the older Surya Siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya. It also contained a description of several astronomical instruments: A third text, which may have survived in the Arabic translation, is Al ntf or Al-nanf.

It claims that it is a translation by Aryabhata, but the Sanskrit name of this work is not known. Direct details of Aryabhata’s work are known only from the Aryabhatiya.

The name “Aryabhatiya” is due to later commentators. Aryabhata himself may not have given it a name. His disciple Bhaskara I calls it Ashmakatantra or the treatise from the Ashmaka.

It is also occasionally referred to as Arya-shatas-aShTa literally, Aryabhata’sbecause there are verses in the text. It is written in the very terse style typical of sutra literature, in which each line is an aid to memory for a complex system. Thus, the explication of meaning is due to commentators. The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries.

The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I Bhashya aryabatiya, c. The Aryabhatiya is also remarkable for its description of relativity of motion. He expressed this relativity thus: The place-value system, first seen in the 3rd-century Bakhshali Manuscriptwas clearly in place in his work. While he did not use a symbol for zerothe French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata’s place-value system as a place holder for the powers of ten with null coefficients.

Aryabbhatiya, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic timeshe used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form. By this rule englisu circumference of a circle with a diameter of 20, can be approached.

After Aryabhatiya was translated into Arabic c. Aryabhata discussed the concept of sine in his work by the name of ardha-jyawhich literally means “half-chord”. For simplicity, people started calling it jya.

When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba.

Arysbhatiya, in Arabic writings, vowels are omitted, and it was abbreviated as jb. Later writers substituted it with jaibmeaning “pocket” or “fold in a garment “.

In Arabic, jiba is a meaningless word. Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinuswhich means “cove” or “bay”; thence comes the English word sine.

This problem was also studied in ancient Chinese mathematics, and its solution is usually referred to as the Chinese remainder theorem. It turns out that the smallest value for N is In general, diophantine equations, such as this, can be notoriously difficult. In AryabhatiyaAryabhata provided elegant results for the summation of series of squares and cubes: Aryabhata’s system of astronomy was called the audAyaka systemin which days are reckoned from udaydawn at lanka or “equator”. Some of his later writings on astronomy, which apparently proposed a second model or ardha-rAtrikAmidnight are lost but can be partly reconstructed from the discussion in Brahmagupta ‘s Khandakhadyaka.

In some texts, he seems to ascribe the apparent motions of the heavens to the Earth’s rotation. He may have believed that the planet’s orbits as elliptical rather than circular. Aryabhata correctly insisted that the earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the earth, contrary to the then-prevailing view, that the sky rotated. In the same way that someone in a boat going forward sees an unmoving [object] going backward, so [someone] on the equator sees the unmoving stars going uniformly westward.

The cause of rising and setting [is that] the sphere of the stars together with the planets [apparently? Aryabhata described a geocentric model of the solar system, in which the Sun and Moon are each carried by epicycles. They in turn revolve around the Earth. The positions and periods of the planets was calculated relative to uniformly moving points. In the case of Mercury and Venus, they move around the Earth at the same mean speed as the Sun. In the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, representing each planet’s motion through the zodiac.

Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy. Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu identified as the pseudo-planetary lunar nodeshe explains eclipses in terms of shadows cast by and falling on Earth.

Thus, the lunar eclipse occurs when the Moon enters into the Earth’s shadow verse gola. He discusses at length the size and extent of the Earth’s shadow verses gola. Later Indian astronomers improved on the calculations, but Aryabhata’s methods provided the core. His computational paradigm was so accurate that 18th-century scientist Guillaume Le Gentilduring a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 30 August to be short by 41 seconds, whereas his charts by Tobias Mayer, were long by 68 seconds.

Considered in modern English units of time, Aryabhata calculated the sidereal rotation the rotation of the earth referencing the fixed stars as 23 hours, 56 minutes, and 4.

Similarly, his value for the length of the sidereal year at days, 6 hours, 12 minutes, and 30 seconds As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on its own axis.

Thus, it has been suggested that Aryabhata’s calculations were based on an underlying heliocentric model, in which the planets orbit the Sun, [35] [36] [37] though this has been rebutted. Aryabhata’s work was of great influence in the Indian astronomical tradition and influenced several neighbouring cultures through translations. The Arabic translation during the Islamic Golden Age c. Some of his results are cited by Al-Khwarizmi and in the 10th century Al-Biruni stated that Aryabhata’s followers believed that the Earth rotated on its axis.

His definitions of sine jyacosine kojyaversine utkrama-jyaand inverse sine otkram jya influenced the birth of trigonometry. In fact, modern names “sine” and “cosine” are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misunderstood by Gerard of Cremona while translating an Arabic geometry text to Latin.

### The Aryabhatiya of Aryabhata – Wikisource, the free online library

He assumed that jiba was translatikn Arabic word jaibwhich means “fold in a garment”, L. Aryabhata’s astronomical calculation methods were also very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world and used to compute many Arabic astronomical tables zijes.

In particular, the astronomical tables in the work of the Arabic Atyabhatiya scientist Al-Zarqali 11th century were translated into Latin as the Tables of Toledo 12th enhlish and remained the most accurate ephemeris used in Europe for centuries. Calendric calculations devised by Aryabhata and his followers have been in continuous use in India for the practical purposes of fixing the Panchangam the Hindu calendar.

In the Islamic world, they formed the basis of the Jalali calendar introduced in CE by a group of astronomers including Omar Khayyam[43] versions of which modified in are the national calendars in use in Iran and Afghanistan today.

Englieh dates of the Jalali calendar are based on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of calendar requires an ephemeris for arabhatiya dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar than in the Gregorian calendar. Aryabhatta Knowledge University AKUPatna has been established by Government of Bihar for the development and management of educational infrastructure related to technical, medical, management and allied professional education in his honour.

The university is governed by Bihar State University Act India’s first satellite Aryabhata and the lunar crater Aryabhata are named in his honour. The inter-school Aryabhata Maths Competition is also named after him, [44] as is Bacillus aryabhataa species of bacteria discovered in the stratosphere by ISRO scientists in From Wikipedia, the free encyclopedia.

For other uses, see Transkation disambiguation.

### Full text of “Aryabhatiya-with-English-commentary”

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Archived from the original on 14 September Archived from the original on 11 July Retrieved 18 July The Britannica Guide to Numbers and Measurement.