Reddit reviews The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World

Don't fret!

Calc and the higher maths are like a video game on paper.

This is a good intro and quite the stirring read.

Hawking's On The Shoulders of Giants

Gribbin's The Scientists

Smithsonian's Timelines of Science

There are also a ton of good historical books on almost every major milestone in physics - a few I enjoyed:

The Clockwork Universe by Edward Dolnick

Faraday, Maxwell, and the Electric Field by Nancy Forbes

E=MC2 by David Bodanis

Quantum by Manjit Kumar

The Big Bang by Simon Singh

I can't link you to any histories of biology or chemistry, sorry, those aren't my areas of knowledge.

to me, the most interesting mathematical history books are those with a targeted goal, meaning they cover the historical aspect of a specific topic, time period, person or group of people, etc. these, at least in my opinion, provide the most insight, as some of the more general books, particular those written for the general public, are too overarching to get much out of. also, another suggestion is to find biographies of mathematicians or physicists. i personally do not find any math history prior to the 1500-1600s or so that interesting, so all of my suggestions are appropriately biased.

a few suggestions are:

• a history of vector analysis by michael j. crowe
  
• isaac newton by james gleick
  
• isaac newton by gale e. christianson
  
• the clockwork universe: isaac newton, the royal society, and the birth of the modern world
  
• gravity by george gamow
  
• one two three ... infinity by george gamow
  
• the mactutor history of mathematics archive - the biographies index is really pretty good and is often a starting point for me.
  
• ams notices - great for finding expository articles and interviews
  
  i don't know of many books that follow the history of a certain subject that are any good. most of my historical knowledge regarding a certain subject is taken from multiple sources. a good method is to read articles, track down the books and/or papers that are referenced by a certain book or paper you like, find biographies of the mathematicians involved, etc. for instance, interviews with mathematicians (like those in the ams notices and the one i posted the other day) are fantastic troves of information regarding the history of certain topics, because the story is being told by a direct participant.

I highly recommend a book called The Clockwork Universe. Not specifically about Leibniz, but discusses him quite a bit (mainly in context with Newton) and is a very accessible read.