Before 1752 the first day of the year was 25 March. So, days of the year that fell from Jan 1 – Mar 25 were notated using the previous year, or double dating. So, both Jan 1, 1600 and the double date Jan 1, 1600/1 matches our Jan 1 in the year 1601. This applies to any English dates from 1752 back in time that fall from Jan 1 through Mar 25. You might see (O.S.) for old style, or (N.S.) for new style added.
Bottom Line: When you see English double date notation such as Jan 1, 1750/1, just remember the later date matches our modern historical date. Prior to 1752, if you see an English date from 1 Jan through 25 Mar, just remember that is toward the end of their year so the actual “year” is the next year unless marked (N.S.).
In particular, you’ll see English double dates used from 1582-1752 in England, Wales, and English colonies such as America. The cause of double dates is because of the transition from the Julian calendar (new year is March 25) to the Gregorian calendar (new year is January 1). Many Catholic countries switched over in 1582 and started using double dates through 1752 on legal documents. Other countries did so at different times. For example, Russia only did so in 1918.