The History of Mathematical Proof in Ancient Traditions

Reading proofs in Chinese commentaries 483 operations with quantities containing fractions are unique to China, by contrast to o ...

484 karine chemla operating on quantities such as a + b/c ( huan, baochu, lianchu ) on the other hand. In that way, these terms ...

Reading proofs in Chinese commentaries 485 ( 2003 ) ‘ Generality above abstraction: the general expressed in terms of the paradi ...

486 karine chemla Peng Hao ( 2001 ) Zhangjiashan Hanjian «Suanshushu» Zhushi (Commentary on the Book on Bamboo Rods from the Han ...

487 14 Dispelling mathematical doubts: assessing mathematical correctness of algorithms in Bhāskara’s commentary on the mathemat ...

488 agathe keller of the verses) will provide a backdrop for refl ections on the mathematical correctness of procedures. Next, t ...

Algorithms in Bhāskara’s commentary on Āryabhat. īya 489 heights? etc.) 4 Bhāskara’s commentary adopts technical words, and the ...

490 agathe keller presents diffi culties. Indeed, the rationale behind the fragmentary argu- ments that BAB sets forth is at tim ...

Algorithms in Bhāskara’s commentary on Āryabhat. īya 491 Th e quotient of that divided by the measure should be this fruit of de ...

492 agathe keller and equilateral triangles have sides ( aśra , for all sides), fl anks ( pārśva , a synonym) and sometimes eart ...

Algorithms in Bhāskara’s commentary on Āryabhat. īya 493 Its computation should be known indeed as the shadow of the gnomon 〈mea ...

494 agathe keller Th e standard formulation of the Rule of Th ree, applied to the similar triangles AFD and DEC, can be recogniz ...

Algorithms in Bhāskara’s commentary on Āryabhat. īya 495 Bhāskara states this relationship by considering the Rule of Th ree: 17 ...

496 agathe keller Now, Bhāskara considers an example for an equinox in which OG = 13, OC = 5 and the radius of the celestial sph ...

Algorithms in Bhāskara’s commentary on Āryabhat. īya 497 employs the Pythagorean Th eorem to compute OS ′ u. In order to identif ...

498 agathe keller Th e mathematical key to both these computations is the prior relation- ship between the gnomon and the celest ...

Algorithms in Bhāskara’s commentary on Āryabhat. īya 499 for the diagonals. Th e procedure is made of a multiplication followed ...

500 agathe keller explanation contains two steps. Th e fi rst step considers the proportionality in a diagram, then ‘reinterpret ...

Algorithms in Bhāskara’s commentary on Āryabhat. īya 501 Note that this passage emphasizes that explanations belong to the genre ...

502 agathe keller hypotenuse of AHC. Bhāskara explains how to compute the upright side by using the Pythagorean Th eorem and the ...