Rivers (1846) p. 131
Our very old Damask Rose, the red monthly, not the comparatively new rose, "rose à quatres saisons" of the French, but the red monthly rose of our oldest writers on gardening, is probably the rose which was cultivated so extensively in Egypt and in Rome for its quality of flowering in autumn.

This passage is in the 1843 edition, but "rose à quatres saisons" is not mentioned.

Here's a translation of Ferrari (The Art of Botany, 1638), courtesy of DistantDrummer:

"From pp. 202-3

The Damask Class (Group)

And of the characteristically faint scented full flower of the Damask Rose, which some including Pliny called the Coroneola or Autumn Rose, and others explained as the Spineola or Littled Spined Rose, the trunk gradually turns darker [dark red or purple literally] from green, and within its multibranched thicket, the verily uncrowded spines arm the growing and extensive canes/stalks with a saturated color, (spines that are) short, hard, dark red, and hooked broadly from the base into bent back thorns/prickles.

The Class of Flowers Tinged with Red or Purple

Of the commonly sown (rose) that lightly turns red from white with dense leaves, which Pliny ascribed as the Alabandican, and other well noted writers called the Trachanian, the canes are shorter and suckering/branching, narrower, somewhat green, usually densely packed with smaller and larger prickles in a dull pale-slate color, and threatening with outstretched points.

The Varigated Double Flowered, The Italian Perpetual Double Flowered

The variety which is spotted with a faint red on its many petaled flower, said to be the Praenestine, is equally bristled with sharp thorns. The Italian variety which always pleasantly turns red, similar to the previous two varieties above, is ferocious with dense prickles.

p.364 (Following discussion of how to care for gallicas)

They say that the Italic (rose) is similar to the previously mentioned rose, however that it is more famous, that it demands careful maintenance [because of? There could be a causal sense to this participle] always being green, that it is perpetual or the rose of all months: because that one, rather often being the first pruned, displays the most tightly packed buds of its flower bunch (inflorescence/spray) to look at all together, which (buds) the variety then opens gradually part by part until another continuous pruning of the flowers [usque is difficult to place in the English, but it gets across the idea that this entire process of deadheading and flowering is continuous]; so that it seems they induce themselves with flowers together in each of the months. Moreover on this matter, the variety differs with a much higher number of buds, and especially by the continuousness of its flowers differs greatly from the previous one, which, less rich [i.e. it is stingy] of its purple bloom, opens more rarely with alabaster colored blooms. The result, therefore, is that the perpetual (variety) shows the signs of spring in all or at least most months, and often during the year it needs to be pruned at least twice. At the end of each October, the whole top (of the plant) is cut back to the ground with a straight cut, so that it might push back from harshness: for having been prepared thus, more numerous buds will over winter with flowery fertility."

An interesting statement is found in 'Colloquies on the Simples and Drugs of India' (1563), written by a Portuguese doctor who'd spent decades there, Garcia da Orta. The end is presented as a dialogue, intended to cover subjects missed in the main text. One of the questions is apparently about Damask roses. From the English translation of 1895, p. 484:

"Ruano

Referring to the way of Ormuz, conversing with the Moors of Persia, they tell me about the Persian roses, so called by Avicenna, which we call acuquare rosado de Alexandria. Are these roses of Persia held to be soluble ? for we find those that are brought and planted to be so.

Orta

That medicine is much used among the inhabitants of Persia and Ormuz. For a man it is a light purgative in a good quantity, and boiled it is stronger. They give it boiled in 10-ounce doses with a little sugar..."

The name of the rose translates as "rosy (or pink) sugar of Alexandria," possibly related to the traditional sales of sugar-coated damask petals as a delicious medicine. The translator footnoted the term "Persian rose," saying it was R. damascena, but didn't explain why. At least one of the references here at HMF says the Autumn Damask has been called the Rose of Alexandria in Spanish, which seems related, and hints at a possible common origin for Damasks on the Iberian peninsula. Avicenna (early 11th century) seems to be the authority da Orta relies on, so may document that Damasks were known in Persia a thousand years ago. So far, in Book 2 of his Canon of Medicine, I've only found reference to Rosa canina and Gol-e Sorkh, the latter of which has been variously translated as R. damascena or R. centifolia, but since it means "red rose," da Orta's statement may be based either on contemporary misunderstanding, or from the damascena reference being in another of Avicenna's works.