August Jäger is listing "Amandine" as a Hybrid Perpetual, bred by Vibert in 1846.
There are 5 different roses with the name "Armide" in Jäger's Lexikon:
Alba by Vibert 1817 ( Frances Gore is listing it as "Armida", page 271)
Noisette by Laffay pre 1836 (Frances Gore, page 366)
Sempervirens pre 1845
Portland by Vibert 1847
Hybrid Perpetual by Morgottin 1858
I'm nearly sure, that "Amandine" and "Armide" are no synonyms. I don't know which of these roses has survived and can be found in our gardens today