Two New Sciences motion and a naturally accelerated vertical motion which produces a parabolic curve. Two motions at right angles can be calculated using the sum of the squares. He shows in detail how to construct the parabolas in various situations and gives tables for altitude and range depending on the projected angle. [274] Air resistance shows itself in two ways: by affecting less dense bodies more and by offering greater resistance to faster bodies. A lead ball will fall slightly faster than an oak ball, but the difference with a stone ball is negligible. However the speed does not go on increasing
Square-free word first difference of the Thue–Morse sequence. That is, from the Thue–Morse sequence one forms a new sequence in which each term is the difference of two consecutive terms of the Thue–Morse sequence. The resulting square-free word is Another example found by John Leech is defined recursively over the alphabet {"a, b, c"}. Let formula_1 be any word starting with the letter "a". Define the words formula_2 recursively as follows: the word formula_3 is obtained from formula_4 by replacing each "a" in formula_4 with , each "b" with , and each "c" with . It is possible to check that the