Gautama Buddha’s teaching of four noble truths and eightfold noble path are called Buddhism.
The four noble truths: dukha or existence of suffering in the world dukha-samudhaya or cause for suffereing dukhanirodha or it is possible to stop suffering dukha-nirodha marga or way out of the suffering.
Eightfold noble path: samyagdrsti or right views samyak-sankalpa or right resolve samyak-karmanta or right conduct samyagjiva or right livelihood samyag-vyayama or right effort samyak-smrti or right mindfulness samyak-samadhi or right concentration
So "the kinship of the religions of India stems from the fact that Jains, Buddhists and Sikhs look back to Hinduism as their common mother."
Main Reasons for Buddhism's Decline in India
Buddhism had always been a monastic or ascetic religion with almost very few lay followers, and so when Islamists had invaded the Indian Subcontinent, and persecuted all Hindus (Buddhists, Jains, Shaivas, etc), due to the loss of Buddhist institutions such as their temples and universities, the outlawing of Hindu asceticism, and the slaughter of Hindu (including of Buddhists) clergy, they had no resources to continue their tradition, and Buddhism waned.
The Taliban of Afghanistan destroying the Buddhist Bamiyan structures of ancient Afghanistan in the early 21st century is no different than how Islamists destroyed Buddhist structures.
- Religions of the World S. Vernon McCasland, Grace E. Cairns, David C. Yu