"Although Rome I s usually called the Successor to Hellenistic Greece, they actually over lapped in time. Chronologically, Rome emerged as a community during the same era a Athens and Sparta, but it did not become important until much later" (PA pg.110). This passage is referring to early Rome and the later Rome. The early Rome did take some of the culture from Greece but over time it developed into a more Roman type of culture it just was not recognized until later time.
The Romans began their conquest over the Greece in 282 B.C.E. after they defeated the Samnites. Defeating the Samnites allowed the Romans come in contact with a new rival the Greek city states of southern Italy. Although the Romans saw the Greeks as, people who were superior to them in ways such as, culture, imagination, and in commerce (buying and selling goods). They also admired the Greeks for their skills in organizing, and governing, and their experience in the world outside of Italy. The Romans still felt that they should Govern and not the Greeks. The Romans felt this way because they saw how the Greek states rise with greatness and later would fall, the Romans saw a cycle and thought the way the Greeks were Governing the state led them to fall ( PR pg. 139 ).
After the Romans defeated the Samnites they wanted to make their allies the Greeks their friends. They did not want to go about it being force full instead they tried to encourage the Greeks to go to Roman culture. They told Greeks that regardless of ethnic or historical affiliations they could still be a Roman Citizen. The Romans gave partial citizenship rights to the Greeks as long as they agreed to not to rebel and to give troops to Rome any time they were needed. Greeks were so eager to citizens that they would marry Romans, adopt the Latin language and accept the Roman custom and law. Going about ruling Italy this way gave Romans the opportunity to learn the Greek culture.