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Two New Sciences. Merged from Talk page.
His theory of tides turned out to be mistaken.
His theory of tides turned out to be mistaken.
==''Dialogues Concerning Two New Sciences''==
Galileo’s last book, the 1638 work ''Discourses Concerning Two New Sciences'', dealt with motion and mechanics. This work helped inspire [[Isaac Newton]] to create his theory of [[gravity]], which linked Galileo’s mathematics and physics to [[Johannes Kepler|Kepler’s]] laws of planetary movement.
Galileo’s last book, the 1638 work ''Discourses Concerning Two New Sciences'', dealt with motion and mechanics. This work helped inspire [[Isaac Newton]] to create his theory of [[gravity]], which linked Galileo’s mathematics and physics to [[Johannes Kepler|Kepler’s]] laws of planetary movement.
[[Image:Galileobones.jpg|right|thumb|200px|Galileo's drawing of how the dimensions of different-sized bones need to vary to make them equally strong]]
In ''Two New Sciences,'' Galileo revealed a sophisticated understanding of engineering and what now would be called [[dimensional analysis]], the way in which the proportions of an engineering structure need to change as the size of the structure is scaled up. He applied this to biology, explaining why the bones of a large animal need to be thicker in proportion to their size than those of smaller animals.
In an age before stopwatches, Galileo was able to make quantitative observations of uniformly-accelerated motion, using his pulse as a time reference and watching the slow acceleration of objects moving down inclined planes.
This book contains his famous discussion and thought experiment, in which he shows both by logic and by appeal to experiment that light and heavy objects fall at the same speed (contradicting Aristotle). One of his discussants says "But I, Simplicio, who have made the test can assure you that a cannon ball weighing one or two hundred pounds, or even more, will not reach the ground by as much as a span ahead of a musket ball weighing only half a pound, provided both are dropped from a height of 200 cubits."<ref>Crew, Henry and Alfonso de Salvio (1914), ''Dialogues Concerning Two New Sciences by Galileo Galilei,'' Northwestern University, 1939 reprint of 1914 Macmillan edition, p. 62</ref>.
Another discussant points out that this result is logical, by positing a large stone that moves at a speed of eight and a smaller one which moves at a speed of four, and showing that this leads to a contradiction if the stones are tied together. Since the smaller stone tends to fall more slowly, it ought to retard the motion of the larger one, so the combination should fall more slowly than the large stone by itself. However, "the two stones when tied together make a stone larger than before," and hence ought to fall more quickly than the large stone by itself.
It is interesting to see how Galileo was able to obtain quantitative results in physics before algebra and calculus were invented. The book uses the methods of geometry, and lays out "proofs" of physical relationships using a style and terminology similar to [[Euclid]]'s Elements.
In 1741, a century after Galileo's death in January 1642, the Church under Pope Benedict XIV bid the Holy Office grant an imprimatur to the first edition of the <i>Complete Works of Galileo</i>.<ref> [http://www.catholiceducation.org/articles/history/world/wh0005.html The Galileo Affair]</ref>
In 1741, a century after Galileo's death in January 1642, the Church under Pope Benedict XIV bid the Holy Office grant an imprimatur to the first edition of the <i>Complete Works of Galileo</i>.<ref> [http://www.catholiceducation.org/articles/history/world/wh0005.html The Galileo Affair]</ref>