Epistle on Verifying the Quantities of Applications

"The Epistle on Verifying the Quantities of Applications" is a work by al-Battani that has not reached us; its title is that of chapter 54 of the Zij. ¹ Ibn al-Nadim called it a well-known epistle of his. ²

Nallino suggests that in it al-Battani may have restored the astrological doctrine of the projection of rays to sound geometrical principles for the first time; Nallino sets out its subject in his notes on chapter 54. ¹

Al-Battani wrote it for Abu al-Hasan Ali ibn Muhammad ibn Musa ibn al-Hasan ibn al-Furat, born on 22 Rabi' II 241, three times vizier to al-Muqtadir and put to death at his order on 13 Rabi' II 312, a patron of poets and of learning. ^{1 2} Nallino counts Ibn al-Furat's request among the signs of the esteem in which al-Battani's contemporaries held him. ³

Nallino rejects the view that it is the same as the Book on Knowing the Ascensions of the Signs, noting that al-Qifti and Ibn Khallikan list the two separately and that the problem of ascensions is quite other than that of applications. ²