Physics history book with some math I am looking for a book explaining physics from, say, Galileo and Newton till now;
the book should be written using some math, similarly to my physics books when
I was at the university (Halliday Resnik). I am searching a book that take care of explaining the true "evolution" of reasoning, discoveries, experiment to prove or disprove something.
I do not like a book that gives definitions without explaining what had happened.
I also like to find, on that book, explanations on how actual measurements are taken
(how can we measure the speed of light, the mass of celestial bodies, the attributes of electron, and how were the measurements taken in the past - how was possible to measure the speed of light in 1700-1800?).
I am not very interested in recent theories like strings, branes.... so it is OK if these are not discussed.
I like to find a lot of discussions on concept that are related, like for instance the implications on space dimensionalities, ether non-existence, strange facts, missing explanations.
 A: Huygens and Barrow, Newton and Hooke by V. I Arnold. 
I havent read it, but I am a fan of the author's writing style. He is a celebrated Russian Mathematician and also one of the most highly cited Russian Scientists. Road to reality (which Im currently reading) would also have been a good suggestion but its pretty much all about recent theories, which you're not interested in.
A: May I suggest "To Explain the World: The Discovery of Modern Science" by S. Weinberg. Weinberg is a theoretical physicist, not a historian, and the focus of the book should meet your criterion. He starts with a guided tour of ancient Greek physics, after which he quickly moved to the scientific revolution in Western Europe during the Renaissance. Weinberg limits himself to astronomy and physics, which are his domain of expertise. Post-Newtonian physics takes the single last chapter, and it feels rather too terse, but he would have needed another book to cover the rise of quantum mechanics, relativity and their offspring, quantum field theory. It should also be noted that the math requested by the OP are separated from the main text, in technical notes gathered at the end of the book.
A: There are two books by Abraham Pais, which are both superb and use enough mathematics to convey the truth of the science.
The first, Subtle is the Lord, is a scientific biography of Einstein.
The second, Inward Bound, tells the story of the development of atomic and particle physics.  It covers roughly the epoch from Curie to Weinberg, stopping just short of Wilson.
Silvan Schweber's QED & the Men Who Made it is also very good and similar in flavor.
It should be noted that both books have a significant flaw, which is that they don't really discuss Ken Wilson's work.  Wilson explained renormalization, which is the physics at the core of quantum field theory.  Much of his predecessors concerns about infinities and the like resulted from doing the computations with unphysical intermediate quantities.  Unfortunately, as far as I know, there is no scientific biography of Wilson.
A: The collection "A course in basic physics" from H. Moysés Nussenzveig is basically a basic physics book with the history as a bonus. Perhaps is what you are looking for. Some chapter focus more in history than others, but all of them have a little bit of the history and experiments behind the discovery.
The course has 4 volumes: Mechanics, Waves and Thermodynamics, Electromagnetism, Optics and Quantum Mechanics.
As for the math, it uses vector calculus, differential equations, and linear algebra. The book itself is not mathematically rigorous, but it gives a much more mathematical treatment of the topics when compared to Halliday & Resnick, for example. 
