Editing Nicolo Tartaglia (section)

==Tartaglia's triangle==
{{main|Tartaglia's triangle}}
[[Image:Tartaglias_Triangle_from_his_General_Trattato.jpg|thumb|Tartaglia's triangle from [https://books.google.com/books?id=EIpIBb38k0AC&pg=PP146 ''General Trattato di Numeri et Misure'', Part II, Book 2, p. 69.]]]
Tartaglia was proficient with binomial expansions and included many worked examples in Part II of the ''General Trattato'', one a detailed explanation of how to calculate the summands of <math>(6 + 4)^7</math>, including the appropriate [[binomial coefficient]]s.<ref>See Tartaglia, Niccolò. [https://books.google.com/books?id=hnFdAAAAcAAJ&pg=PP112 ''General Trattato di Numeri et Misure'', Part II, Book 2, p. 51v] for expanding <math>(6 + 4)^7</math>.</ref>

Tartaglia knew of [[Pascal's triangle]] one hundred years before Pascal, as shown in this image from the ''General Trattato''. His examples are numeric, but he thinks about it geometrically, the horizontal line <math>ab</math> at the top of the triangle being broken into two segments <math>ac</math> and <math>cb</math>, where point <math>c</math> is the apex of the triangle. Binomial expansions amount to taking <math>(ac+cb)^n</math> for exponents <math>n = 2, 3, 4, \cdots</math> as you go down the triangle. The symbols along the outside represent powers at this early stage of algebraic notation: <math>ce = 2, cu = 3, ce.ce = 4</math>, and so on. He writes explicitly about the additive formation rule, that (for example) the adjacent 15 and 20 in the fifth row add up to 35, which appears beneath them in the sixth row.<ref>See Tartaglia, Niccolò. [https://books.google.com/books?id=hnFdAAAAcAAJ&pg=PP112 ''General Trattato di Numeri et Misure'', Part II, Book 2, p. 72] for discussion of the additive rule in "Pascal's triangle".</ref>