Tiantai, also known as the Tendai school, is a Mahayana Buddhist tradition that originated in China and was founded by the Chinese monk Zhiyi in the 6th century. One of the key principles of Tiantai is the integration of all Buddhist teachings around the Lotus Sutra, which is considered the highest and most comprehensive teaching of the Buddha. However, Tiantai also incorporates the teachings of other Buddhist figures, such as Nagarjuna and Vasubandhu, to further enhance its understanding of the Lotus Sutra.

Nagarjuna, a renowned Indian Buddhist philosopher, is known for his teachings on the concept of emptiness and the Middle Way. His philosophy greatly influenced Tiantai, particularly in its understanding of the ultimate reality and the interdependence of all phenomena. Tiantai also adopted Nagarjuna's concept of the "two truths," which distinguishes between conventional truth and ultimate truth, and integrated it into their interpretation of the Lotus Sutra.

Similarly, Vasubandhu, another Indian Buddhist philosopher, is highly revered in Tiantai for his teachings on the nature of consciousness and the mind. His concept of the "eight consciousnesses" is incorporated into Tiantai's understanding of the human mind and its relationship to the ultimate truth. Tiantai also adopted Vasubandhu's teachings on the threefold truth, which states that all phenomena can be understood as either conventional, ultimate, or both.

Incorporating the teachings of Nagarjuna and Vasubandhu into Tiantai's understanding of the Lotus Sutra allows for a more comprehensive and nuanced interpretation of the sutra. Tiantai recognizes that the Lotus Sutra is a vast and profound teaching that cannot be fully understood through one single perspective. By incorporating the teachings of other Buddhist figures, Tiantai is able to deepen its understanding of the Lotus Sutra and present a more complete view of its teachings.

Furthermore, Tiantai also acknowledges the importance of the historical Buddha, Shakyamuni, and his previous teachings. The Lotus Sutra is seen as the culmination and ultimate expression of the Buddha's teachings, and Tiantai recognizes the value of all the teachings that came before it. This inclusive approach to the Lotus Sutra allows Tiantai to integrate the teachings of other Buddhist figures while still maintaining the centrality of the sutra.

In conclusion, Tiantai incorporates the teachings of Nagarjuna and Vasubandhu into its understanding of the Lotus Sutra, recognizing their contributions to Buddhist philosophy and their relevance to the sutra. This integration of various teachings allows Tiantai to present a more comprehensive and holistic interpretation of the Lotus Sutra, further emphasizing its importance in the Buddhist tradition.