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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| History of science | 5/19 | https://en.wikipedia.org/wiki/History_of_science | reference | science, encyclopedia | 2026-05-05T03:38:18.549055+00:00 | kb-cron |
==== Logic ==== The development of Indian logic dates back to the Chandahsutra of Pingala and anviksiki of Medhatithi Gautama (c. 6th century BCE); the Sanskrit grammar rules of Pāṇini (c. 5th century BCE); the Vaisheshika school's analysis of atomism (c. 6th century BCE to 2nd century BCE); the analysis of inference by Gotama (c. 6th century BCE to 2nd century CE), founder of the Nyaya school of Hindu philosophy; and the tetralemma of Nagarjuna (c. 2nd century CE). Indian logic stands as one of the three original traditions of logic, alongside the Greek and the Chinese logic. The Indian tradition continued to develop through early to modern times, in the form of the Navya-Nyāya school of logic. In the 2nd century, the Buddhist philosopher Nagarjuna refined the Catuskoti form of logic. The Catuskoti is also often glossed Tetralemma (Greek) which is the name for a largely comparable, but not equatable, 'four corner argument' within the tradition of Classical logic. Navya-Nyāya developed a sophisticated language and conceptual scheme that allowed it to raise, analyse, and solve problems in logic and epistemology. It systematised all the Nyāya concepts into four main categories: sense or perception (pratyakşa), inference (anumāna), comparison or similarity (upamāna), and testimony (sound or word; śabda).
=== China ===
==== Chinese mathematics ====
From the earliest the Chinese used a positional decimal system on counting boards in order to calculate. To express 10, a single rod is placed in the second box from the right. The spoken language uses a similar system to English: e.g. four thousand two hundred and seven. No symbol was used for zero. By the 1st century BCE, negative numbers and decimal fractions were in use and The Nine Chapters on the Mathematical Art included methods for extracting higher order roots by Horner's method and solving linear equations and by Pythagoras' theorem. Cubic equations were solved in the Tang dynasty and solutions of equations of order higher than 3 appeared in print in 1245 CE by Ch'in Chiu-shao. Pascal's triangle for binomial coefficients was described around 1100 by Jia Xian. Although the first attempts at an axiomatization of geometry appear in the Mohist canon in 330 BCE, Liu Hui developed algebraic methods in geometry in the 3rd century CE and also calculated pi to 5 significant figures. In 480, Zu Chongzhi improved this by discovering the ratio
355
113
{\displaystyle {\tfrac {355}{113}}}
which remained the most accurate value for 1200 years.
==== Astronomical observations ====
Astronomical observations from China constitute the longest continuous sequence from any civilization and include records of sunspots (112 records from 364 BCE), supernovas (1054), lunar and solar eclipses. By the 12th century, they could reasonably accurately make predictions of eclipses, but the knowledge of this was lost during the Ming dynasty, so that the Jesuit Matteo Ricci gained much favor in 1601 by his predictions. By 635 Chinese astronomers had observed that the tails of comets always point away from the sun. From antiquity, the Chinese used an equatorial system for describing the skies and a star map from 940 was drawn using a cylindrical (Mercator) projection. The use of an armillary sphere is recorded from the 4th century BCE and a sphere permanently mounted in equatorial axis from 52 BCE. In 125 CE Zhang Heng used water power to rotate the sphere in real time. This included rings for the meridian and ecliptic. By 1270 they had incorporated the principles of the Arab torquetum. In the Song Empire (960–1279) of Imperial China, Chinese scholar-officials unearthed, studied, and cataloged ancient artifacts.
==== Inventions ====