Did buddhism "triumph" in china in the same sense in which christianity triumphed in the roman world? compare china to the roman empire. what problems did both empires face, and how did they try to resolve them?

No.

Explanation:

This religion had its growth interrupted in India, with the advancement of Islam and the formation of the Great Arab Empire.  Wich has had a strong influence in chinese artistic manifestations, such literature, pinture and esculpture. In Rome, its its significant growth in the IV CENTURY, christianity was considered the official religion of the roman empire.

In Buddhism, its philosophy is based on the existence of being this related to pain, and to overcome pain, man has five paths: correct understanding, correct thinking, word, action, way of life, effort, attention and meditation.  

In Christianity, today considered the religion with the greatest number of supporters in the world, through Christ, his Savior, who rose to the third day, promises salvation and life after death to all those who obey and follow his commandments.

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