Astroज्योतिष

Today's teaching

“Wealth is the star for wealth; what will the stars do?”
— Kautilya, Arthashastra IX.4

Library · Teachers · Aryabhata · born 476 CE, wrote about 499 CE

Aryabhata: the Aryabhatiya

Everything Aryabhata taught, verse by verse, in plain English: his numbers for the universe, his mathematics, his reckoning of time and his sphere — the rotating Earth, the eclipses, π — with what he got right, what he got wrong, and how later astronomers received him. 8 chapters, 10,642 words.

  1. Aryabhata and his bookWho Aryabhata was, when and where he wrote, how his short book is built, the English translation used here, and how to read this book.1,099 words
  2. The numbers of the universeThe Dasagitika: Aryabhata's code for writing numbers in syllables, the revolutions of every planet in an age of the world, the cycles of time, the sizes of Earth, Sun and Moon, the inclinations, nodes and apsides, the epicycles and the sine table — and how accurate the numbers are.1,543 words
  3. Numbers, squares and shapesGanita 1–10: the decimal names of numbers, squares and cubes, Aryabhata's methods for square and cube roots worked step by step, areas of triangles, circles and other figures, two volume rules that are wrong, and his famous value of π.1,133 words
  4. Sines, shadows and trianglesGanita 11–18: how to build a table of sines and Aryabhata's rule for its differences, the instruments of the astronomer, the gnomon and its shadow, the theorem of the right triangle, and overlapping circles — the geometry behind every eclipse calculation.1,207 words
  5. Series, equations and the pulveriserGanita 19–33: sums of series (including squares and cubes), solving for unknowns, interest, the rule of three, fractions, working backwards, the meeting of two planets, and the kuttaka or 'pulveriser' — Aryabhata's method for equations in whole numbers, and why astronomers needed it.1,534 words
  6. The reckoning of timeThe Kalakriya: units of time and space, conjunctions and cycles, the kinds of year, month and day, intercalary months, the ages of gods and men, Aryabhata's own date, the order of the planets and how it gives the days of the week, and his epicycle model of planetary motion.1,588 words
  7. The sphere of the heavensThe Gola: the ecliptic and the nodes, visibility near the Sun, the round Earth and its rotation (the moving boat), the traditional cosmology of Meru beside the scientific one, longitudes from Lanka and Ujjain, the self-turning armillary sphere, the spherical astronomy of day length and shadows, and the full theory and calculation of eclipses.1,651 words
  8. What Aryabhata got right and wrongAn honest balance sheet: Aryabhata's achievements and his errors, how Brahmagupta, Bhaskara I, the Kerala school and al-Biruni received him, the small error in his year and what it did over the centuries, and what his book is — and is not — for a student of Jyotisha.887 words

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