maw?q?t and recently found rules

having briefly been reviewed the historical process of changing the formulae for determining the times of islamic prayers, two newly found formulae and a new rule for establishing the times of prayers would be discussed. these matters have been exploited from four texts, still preserved as manuscript: (1) siyyid ¾?y? al-d?n sh?shtar?’s ¼ad b?b dar macrifa al-a½??rl?b, (2) b?r?n?’s ’ist?c?b f? cilm al-a½??rl?b, (3) mu¬ammad madjd al-d?n b. zayn al-d?n mu¬ammad hamid?n?’s ’an?s al-?ull?b f? macrifa al-a½?url?b, and (4) an anonymous treatise named al-’ist?c?b li-’l-camal bi-¼adr al-waza wa-’l-jin?¬ al-ghur?b. in the end, the accuracy of the numeral results derived from those formulae would be presented, by making a comparison with each other as well as with the standard rules.