The Roman Method of counting the Days of the Month.
Church History (Historia Ecclesiastica) · Eusebius of Caesarea
“Instead of distinguishing the days by the ordinal numbers, first, second, third, etc., the Romans counted backwards from three fixed epochs; namely, the Kalends, the Nones, and the Ides. The Kalends were invariably the first day of the month, and were so denominated because it had been an ancient custom of the pontiffs to call the people together on that day, to apprise them of the festivals, or days that were to be kept sacred during the month. The Ides (from an obsolete verb iduare, to divide) were at the middle of the month, either the 13th or the 15th day; and the Nones were the ninth day before the Ides, counting inclusively. From these three terms the days received their denomination in the following manner:—
EusHE 14.29.167
“Those which were comprised between the Kalends and the Nones were called the days before the Nones; those between the Nones and the Ides were called the days before the Ides; and, lastly, all the days after the Ides to the end of the month were called the days before the Kalends of the succeeding month.
EusHE 14.29.168
“In the months of March, May, July, and October, the Ides fell on the 15th day, and the Nones consequently on the 7th: so that each of these months had six days named from the Nones. In all the other months the Ides were on the 13th and the Nones were on the 5th; consequently there were only four days named from the Nones. Every month had eight days named from the Ides. The number of days receiving their denomination from the Kalends depended on the number of days in the month and the day on which the Ides fell. For example, if the month contained 31 days, and the Ides fell on the 13th as was the case in January, August, and December, there would remain 18 days after the Ides, which, added to the first of the following month, made 19 days of Kalends. In January, therefore, the 14th day of the month was called the nineteenth before the Kalends of February (counting inclusively), the 15th was the 18th before the Kalends, and so on to the 30th, which was called the third before the Kalends (tertio Kalendas), the last being the second of the Kalends, or the day before the Kalends (pridie Kalendas).”
EusHE 14.29.169