How did the "dog days of summer" enter the English language?

Solution 1:

An earlier term was canicular days, variously spelled. This term still surfaces from time to time, although mostly as a novelty (as in this 2011 Space.com article) or as the peculiar choice of some or other translation dictionary (as in the title of this 2015 acupuncture paper, 三伏天 being rendered in some citations as dog days or dog days of summer).

The OED has it from Latin, akin to the French caniculaire, from 1398 in John Trevisa's translation of the friar Bartholomew de Glanville's De Proprietatibus Rerum:

In the mydle of the monthe Iulius the Canicular dayes begyn.

The next is from Richard Arnold's Chronicle, ca. 1503:

The Canycular daies begynne ye xv kalendas of august and endure to the iiij. nonas of septembre.

There is an explanatory note on the differing dates:

The dog days have been variously reckoned, as depending on either the Greater Dog Star (Sirius) or the Lesser Dog Star (Procyon), and on either the heliacal rising or the cosmical rising (which occurs at an earlier date). The timing of these risings depends on latitude, and they do not occur at all in most of southern hemisphere; in addition, owing to the precession of the equinox they now take place later in the year. As a result very different dates have been assigned for the dog days, their beginning ranging from 3 July to 15 August, and their duration varying from 30 to 61 days. In the Calendar of the 1552 Book of Common Prayer they run from 7 July to 5 September. In current calendars they are often said to begin on 3 July and end on 11 August (i.e. the 40 days preceding the cosmical rising of Sirius at the latitude of Greenwich).

The earliest entry for dog days appears in Thomas Elyot's 1538 dictionary as

Canicula..a sterre, wherof canicular or dogge days be named Dies caniculares.

The shorter, alliterative variant no doubt supplanted the Latinate word over time, though it is difficult to ascertain when using online tools.