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Brahmagupta: Revision history

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30 June 2024

7 June 2024

31 May 2024

  • curprev 22:2622:26, 31 May 2024‎ Yue talk contribs‎ m 45,616 bytes −116‎ Reverted edit by 63.153.141.228 (talk) to last version by RegentsPark undo Tag: Rollback [automatically accepted]
  • curprev 21:4921:49, 31 May 2024‎ 63.153.141.228 talk‎ 45,732 bytes +116‎ →‎Early concept of gravity (a laughable presentism shoehorning "gravity" into the following text, which has nothing to do with alleged gravity) undo Tags: Reverted Mobile edit Mobile web edit
  • curprev 14:3514:35, 31 May 2024‎ RegentsPark talk contribs‎ 45,616 bytes +25,533‎ Restored revision 1226557934 by Egsan Bacon (talk): Rvt undo Tags: Twinkle Undo [automatically accepted]
  • curprev 14:0614:06, 31 May 2024‎ 103.190.8.224 talk‎ 20,083 bytes −36‎ Citations Pickover, Clifford (2008). Archimedes to Hawking: Laws of Science and the Great Minds Behind Them. Oxford University Press. p. 105. ISBN 978-0-19-979268-9. Bose, Mainak Kumar (1988). Late classical India. A. Mukherjee & Co.[page needed] Sen, Amartya (2005). The Argumentative Indian. Allen Lane. p. 29. ISBN 978-0-7139-9687-6. Thurston, Hugh (1993). Early Astronomy. New York: Springer-Verlag. ISBN 978-0-387-94107-3.[page needed][failed verification] Bradley, Michael. The Birth of M undo Tags: Reverted section blanking Visual edit Mobile edit Mobile web edit
  • curprev 14:0314:03, 31 May 2024‎ 103.190.8.224 talk‎ 20,119 bytes −1,931‎ In chapter seven of his Brāhmasphuṭasiddhānta, entitled Lunar Crescent, Brahmagupta rebuts the idea that the Moon is farther from the Earth than the Sun. [clarification needed] He does this by explaining the illumination of the Moon by the Sun. 1. If the moon were above the sun, how would the power of waxing and waning, etc., be produced from calculation of the longitude of the moon? The near half would always be bright. 2. In the same way that the half seen by the sun of a pot standing in su undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 14:0214:02, 31 May 2024‎ 103.190.8.224 talk‎ 22,050 bytes −1,391‎ The earth on all its sides is the same; all people on the earth stand upright, and all heavy things fall down to the earth by a law of nature, for it is the nature of the earth to attract and to keep things, as it is the nature of water to flow ... If a thing wants to go deeper down than the earth, let it try. The earth is the only low thing, and seeds always return to it, in whatever direction you may throw them away, and never rise upwards from the earth. undo Tags: Reverted references removed Visual edit Mobile edit Mobile web edit
  • curprev 14:0114:01, 31 May 2024‎ 103.190.8.224 talk‎ 23,441 bytes −2,108‎ 2.2–5. The sines: The Progenitors, twins; Ursa Major, twins, the Vedas; the gods, fires, six; flavors, dice, the gods; the moon, five, the sky, the moon; the moon, arrows, suns [...] Here Brahmagupta uses names of objects to represent the digits of place-value numerals, as was common with numerical data in Sanskrit treatises. Progenitors represents the 14 Progenitors ("Manu") in Indian cosmology or 14, "twins" means 2, "Ursa Major" represents the seven stars of Ursa Major or 7, "Vedas" refers t undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 14:0014:00, 31 May 2024‎ 103.190.8.224 talk‎ 25,549 bytes −1,208‎ After giving the value of pi, he deals with the geometry of plane figures and solids, such as finding volumes and surface areas (or empty spaces dug out of solids). He finds the volume of rectangular prisms, pyramids, and the frustum of a square pyramid. He further finds the average depth of a series of pits. For the volume of a frustum of a pyramid, he gives the "pragmatic" value as the depth times the square of the mean of the edges of the top and bottom faces, and he gives the "superficial" v undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 14:0014:00, 31 May 2024‎ 103.190.8.224 talk‎ 26,757 bytes −1,501‎ Brahmagupta continues, 12.23. The square-root of the sum of the two products of the sides and opposite sides of a non-unequal quadrilateral is the diagonal. The square of the diagonal is diminished by the square of half the sum of the base and the top; the square-root is the perpendicular [altitudes]. So, in a "non-unequal" cyclic quadrilateral (that is, an isosceles trapezoid), the length of each diagonal is √pr + qs. He continues to give formulas for the lengths and areas of geometric figur undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 13:5913:59, 31 May 2024‎ 103.190.8.224 talk‎ 28,258 bytes −1,223‎ 12.21. The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral. The accurate [area] is the square root from the product of the halves of the sums of the sides diminished by [each] side of the quadrilateral. So given the lengths p, q, r and s of a cyclic quadrilateral, the approximate area is p + r/2 · q + s/2 while, letting t = p + q + r + s/2, the exact area is √(t − p)(t − q)(t − r)(t − s). Although Brahmagupta does not undo Tags: Reverted references removed Visual edit Mobile edit Mobile web edit
  • curprev 13:5813:58, 31 May 2024‎ 103.190.8.224 talk‎ 29,481 bytes −2,844‎ Using his identity and the fact that if (x1, y1) and (x2, y2) are solutions to the equations x2 − Ny2 = k1 and x2 − Ny2 = k2, respectively, then (x1x2 + Ny1y2, x1y2 + x2y1) is a solution to x2 − Ny2 = k1k2, he was able to find integral solutions to Pell's equation through a series of equations of the form x2 − Ny2 = ki. Brahmagupta was not able to apply his solution uniformly for all possible values of N, rather he was only able to show that if x2 − Ny2 = k has an integer solution for k = ±1, ±2 undo Tags: Reverted references removed Visual edit Mobile edit Mobile web edit
  • curprev 13:5713:57, 31 May 2024‎ 103.190.8.224 talk‎ 32,325 bytes −1,568‎ 12.39. The height of a mountain multiplied by a given multiplier is the distance to a city; it is not erased. When it is divided by the multiplier increased by two it is the leap of one of the two who make the same journey. Or, in other words, if d = mx/x + 2, then a traveller who "leaps" vertically upwards a distance d from the top of a mountain of height m, and then travels in a straight line to a city at a horizontal distance mx from the base of the mountain, travels the same distance as one undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 13:5613:56, 31 May 2024‎ 103.190.8.224 talk‎ 33,893 bytes −6,594‎ multiplicand is repeated like a string for cattle, as often as there are integrant portions in the multiplier and is repeatedly multiplied by them and the products are added together. It is multiplication. Or the multiplicand is repeated as many times as there are component parts in the multiplier. Indian arithmetic was known in Medieval Europe as modus Indorum meaning "method of the Indians". In the Brāhmasphuṭasiddhānta, four methods for multiplication were described, including gomūtrikā, whi undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 13:5613:56, 31 May 2024‎ 103.190.8.224 talk‎ 40,487 bytes −3,286‎ 18.44. Diminish by the middle [number] the square-root of the rupas multiplied by four times the square and increased by the square of the middle [number]; divide the remainder by twice the square. [The result is] the middle [number]. 18.45. Whatever is the square-root of the rupas multiplied by the square [and] increased by the square of half the unknown, diminished that by half the unknown [and] divide [the remainder] by its square. [The result is] the unknown. which are, respectively, soluti undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 13:5513:55, 31 May 2024‎ 103.190.8.224 talk‎ 43,773 bytes −1,843‎ Bhillamala was the capital of the Gurjaradesa, the second-largest kingdom of Western India, comprising southern Rajasthan and northern Gujarat in modern-day India. It was also a centre of learning for mathematics and astronomy. He became an astronomer of the Brahmapaksha school, one of the four major schools of Indian astronomy during this period. He studied the five traditional Siddhantas on Indian astronomy as well as the work of other astronomers including Aryabhata I, Latadeva, Pradyumna, Va undo Tags: Manual revert Reverted Visual edit Mobile edit Mobile web edit
  • curprev 12:0812:08, 31 May 2024‎ Egsan Bacon talk contribs‎ 45,616 bytes +15,726‎ Reverted 5 pending edits by 103.190.8.224 to revision 1226520275 by CycloneYoris: unexplained removal of a great deal of material undo Tag: Manual revert [automatically accepted]
  • curprev 12:0412:04, 31 May 2024‎ 103.190.8.224 talk‎ 29,890 bytes −1,568‎ 12.39. The height of a mountain multiplied by a given multiplier is the distance to a city; it is not erased. When it is divided by the multiplier increased by two it is the leap of one of the two who make the same journey. Or, in other words, if d = mx/x + 2, then a traveller who "leaps" vertically upwards a distance d from the top of a mountain of height m, and then travels in a straight line to a city at a horizontal distance mx from the base of the mountain, travels the same distance as one undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 12:0312:03, 31 May 2024‎ 103.190.8.224 talk‎ 31,458 bytes −6,621‎ The multiplicand is repeated like a string for cattle, as often as there are integrant portions in the multiplier and is repeatedly multiplied by them and the products are added together. It is multiplication. Or the multiplicand is repeated as many times as there are component parts in the multiplier. Indian arithmetic was known in Medieval Europe as modus Indorum meaning "method of the Indians". In the Brāhmasphuṭasiddhānta, four methods for multiplication were described, including gomūtrikā, undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 12:0312:03, 31 May 2024‎ 103.190.8.224 talk‎ 38,079 bytes −3,286‎ 18.44. Diminish by the middle [number] the square-root of the rupas multiplied by four times the square and increased by the square of the middle [number]; divide the remainder by twice the square. [The result is] the middle [number]. 18.45. Whatever is the square-root of the rupas multiplied by the square [and] increased by the square of half the unknown, diminished that by half the unknown [and] divide [the remainder] by its square. [The result is] the unknown. which are, respectively, soluti undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 11:5911:59, 31 May 2024‎ 103.190.8.224 talk‎ 41,365 bytes −2,408‎ few decades after the death of Brahmagupta, Sindh came under the Arab Caliphate in 712 CE. Expeditions were sent into Gurjaradesa ("Al-Baylaman in Jurz", as per Arab historians). The kingdom of Bhillamala seems to have been annihilated but Ujjain repulsed the attacks. The court of Caliph Al-Mansur (754–775) received an embassy from Sindh, including an astrologer called Kanaka, who brought (possibly memorised) astronomical texts, including those of Brahmagupta. Brahmagupta's texts were translated undo Tags: Reverted references removed Visual edit Mobile edit Mobile web edit
  • curprev 11:5811:58, 31 May 2024‎ 103.190.8.224 talk‎ 43,773 bytes −1,843‎ Bhillamala was the capital of the Gurjaradesa, the second-largest kingdom of Western India, comprising southern Rajasthan and northern Gujarat in modern-day India. It was also a centre of learning for mathematics and astronomy. He became an astronomer of the Brahmapaksha school, one of the four major schools of Indian astronomy during this period. He studied the five traditional Siddhantas on Indian astronomy as well as the work of other astronomers including Aryabhata I, Latadeva, Pradyumna, Va undo Tags: Reverted Visual edit Mobile edit Mobile web edit
  • curprev 04:3004:30, 31 May 2024‎ CycloneYoris talk contribs‎ 45,616 bytes +918‎ Reverted 2 pending edits by 2405:201:9009:91D3:D929:586B:D6FC:57D6 to revision 1222658479 by CycloneYoris undo Tag: Manual revert [automatically accepted]
  • curprev 04:1404:14, 31 May 2024‎ 2405:201:9009:91d3:d929:586b:d6fc:57d6 talk‎ 44,698 bytes −906‎ →‎Algebra undo Tags: Reverted references removed
  • curprev 04:1404:14, 31 May 2024‎ 2405:201:9009:91d3:d929:586b:d6fc:57d6 talk‎ 45,604 bytes −12‎ →‎Algebra undo Tag: Reverted

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