"by appearing to segue into 'rosemary', which is a herb allied to mint"
Puzzled me to, especially as the next entry in the dictionary is "rosemary".
Taking up a bit more space - below is from Rev. Thisleton Dyer's 'Folk Lore of Shakespeare d. 1883, indexed as "customs connected with roses".

Steve;
Will reply later.
Jim Carroll

Rose.—As might be expected, the rose is the flower most | frequently mentioned by Shakespeare; denoting in many cases the symbol of all that is fair and lovely. Thus, for instance, in " Hamlet " (iii. 4), the queen says :—
Such an act….        takes off the rose
From the fair forehead of an innocent love,
And sets a blister there."

And Ophelia (iii. 1), describes Hamlet as—

" The expectancy and rose of the fair state."

In days gone by the rose entered largely into the customs and superstitions of most nations, and even now-a-days there is an extensive folklore associated with it.
It appears that in Shakspeare's time one of the fashions of the day was the wearing of enormous roses on the shoes, of which full-length portraits afford striking examples. Hamlet (iii. 2) speaks " of two provincial roses on his razed shoes."— meaning, no doubt, rosettes of ribbon in the shape of roses of Provins or Provence. Douce favours the former, Warton the latter locality. In either case it was a large rose. The Province or damask rose, was probably the better known.
Gerarde in his " Herbal," says that the damask rose is called by some "Rosa provincialis." Mr Fairholt quotes from Friar Bacon's Prophecy, 1604, the following in allusion to this fashion:—

" When roses in the gardens grew,
And not in ribbons on a shoe:
Now ribbon roses take such place
That garden roses want their grace."

Again, in King John (i. 1), where the Bastard alludes to the three-farthing silver pieces of Queen Elizabeth, which were extremely thin, and had the profile of the sovereign, with a rose on the back of her head, there doubtless is . A fuller reference to the court fashion of sticking roses in the ear:—

"My face so thin,
That in mine ear I durst not stick a rose,
Lest men should say, ' Look, where three-farthings goes.' "

Shakspeare also mentions the use of the rose, in rose-cakes and rose-water, the former in "Romeo and Juliet" (v. I), where Romeo speaks of " old cakes of roses," the latter in " Taming the Shrew " (induction, sc. 1):—

Let one attend him with a silver basin
Full of rose water and bestrewed with flowers."

Plants.
Referring to its historical lore, we may mention its famous connection with the "Wars of the Roses." In the fatal dis-
pute in the Temple Gardens,'Somerset, on the part of Lancaster, says,
(" I Henry VI." ii. 3) :—

" Let him that is no coward nor no flatterer,
But dare maintain the party of the truth,
Pluck a red rose from off this thorn with me."

Warwick, 011 the part of York, replies :—
" I have no colours, and without all colour
Of base insinuating flattery
I pluck this white rose with Plantagenet."

The trailing white dog-rose is commonly considered to have been the one chosen by the house of York. A writer however, in the " Quarterly Review " (vol. cxiv.), has shown that the white rose has a very ancient interest for Englishmen, as, long before the brawl in the Temple Gardens, the flower had been connected with one of the most ancient names of our island. The elder Pliny, in discussing the etymology of the word Albion, suggests that the land may have been so named from the white roses which abounded in it. The York and Lancaster rose, with its pale striped flowers, is a variety of the French rose known as Rosa Gallica. It became famous when the two emblematical roses, in the persons of Henry VII. and Elizabeth of York at last brought peace and happiness to the country which had been so long divided by internal warfare. The canker rose referred to by Shakspeare is the wild dog rose, a name occasionally applied to the common red poppy.