The small or large rock will fall to the Earth along the path of a line that is perpendicular to the plane (sath) of the horizon; this is witnessed by experience (tajriba). And this perpendicular is away from the tangent point of the Earth's sphere and the plane of the perceived (hissi) horizon. This point moves with the motion of the Earth and thus there will be no difference in place of fall of the two rocks.
Al-Birjandi wrote some more than 13 books and treatises, including:
Sharh al-tadhkirah (A commentary on al-Tusi's memoir). The text, in some copies of the manuscript from 17th century, is written throughout in black and red ink with diagrams illustrating many of the astronomical elements discussed. The 11th chapter of the book was translated to Sanskrit in 1729 at Jaipur by Nayanasukhopadhyaya. Kusuba and Pingree present an edition of the Sanskrit, and in a separate section, an English translation facing the Arabic original. That chapter has attracted attention among European scholars since the late 19th century. Al-Birjandi on Tadhkira II, Chapter 11, and Its Sanskrit Translation by Kusuba K. and Pingree D.ISBN978-90-04-12475-2 was published in 2001 by Brill Academic Publishers.
Sharh-i Bist Bab dar Ma'rifat-i A'mal-i al-Asturlab (Commentary on "Twenty Chapters Dealing with the Uses of the Astrolabe" of Nasir al-Din al-Tusi; Persian.
Risalah fi Alat al-Rasad (Epistle on observational instruments); in Arabic.
Tadhkirat al-Ahbab fi Bayan al-Tahabub (Memoir of friends: concerning the explanation of friendship [of numbers]); in Arabic.