When machiavelli wrote the prince in 1513, he faced a lot of criticism. what were the key ideas of the book called the prince, and how did these ideas influence european rulers?

The key ideas were about power and how leaders specifically princes could seek to gain power and also how they could go about maintaining power. These ideas helped to influence European rulers and individuals around the world by promoting this particular type of leadership and power seeking. Hope this helps, good luck. 

radioactive dating, also known as  radioisotope dating  is a process that in  estimating the approximate  age  of  rocks. these data can be analyzed from  the studies dealing with the  decay of the radioactive elements that are present in these rocks. in nature, there are a few types of materials or atoms which are quite unstable and they spontaneously decay or breakdown to form other kinds of atoms.

i dont have that book