Valmiki Ramayana Kishkindha Kanda Sarga 40 Shloka 63

पूर्वम् east, एतत् this, पृथिव्याः earth's, भुवनस्य for the world, द्वारम् entrance, सूर्यस्य Sun's, उदयनं च rise also, कृतम् was made, एषा this, पूर्वा दिक् eastern direction, उच्यते is being called.

'Here is the entrance for the earth as well as for all the worlds and since the Sun also rises from this place it is called the eastern direction.