to 5, 2, 7 and changed remainder to modulo, but apparently still required many trials. The specific cycles used by Scaliger to form his tricyclic Julian Period were, first, the indiction cycle with a first year of 313. Then he chose the dominant 19-year Alexandrian lunar cycle with a first year of 285, the Era of Martyrs and the Diocletian Era epoch, or a first year of 532 according to Dionysius Exiguus. Finally, Scaliger chose the post-Bedan solar cycle with a first year of 776, when its first quadrennium of concurrents, , began in sequence. Although not their intended use, the equations of de Billy or Gauss can be used to determined the first year of any 15-, 19-, and 28-year tricyclic period given any first years of their cycles. For those of the Julian Period, the result is AD3268, because both remainder and modulo usually return the lowest positive result. Thus 7980years must be subtracted from it to yield the first year of the present Julian Period, −4712 or 4713BC, when all three of its sub-cycles are in their first years. Scaliger got the idea of using a tricyclic period from "the Greeks of Constantinople" as Herschel stated in his quotation below in Julian day numbers. Specifically, the monk and priest Georgios wrote in 638/39 that the Byzantine year 6149 AM (640/41) had indiction 14, lunar cycle 12, and solar cycle 17, which places the first year of the Byzantine Era in 5509/08BC, the Byzantine Creation. Dionysius Exiguus called the Byzantine lunar cycle his "lunar cycle" in argumentum 6, in contrast with the Alexandrian lunar cycle which he called his "nineteen-year cycle" in argumentum 5. Although many references say that the Julian in "Julian Period" refers to Scaliger's father, Julius Scaliger, at the beginning of Book V of his ("Work on the Emendation of Time") he states, "", which Reese, Everett and Craun translate as "We have termed it Julian because it fits the Julian year." Thus Julian refers to the Julian calendar. Julian day numbers Julian days were first used by Ludwig Ideler for the first days of the Nabonassar and Christian eras in his 1825 Handbuch der mathematischen und technischen Chronologie. John F. W. Herschel then developed them for astronomical use in his 1849 Outlines of Astronomy, after acknowledging that Ideler was his guide. At least one mathematical astronomer adopted Herschel's "days of the Julian period" immediately.