I’m not familiar with the history of philosophical education, so I don’t know to what extent the text linked to here is original. It struck me as interesting that it is presented in the author, Mrs Phelps’s preface as a somewhat daring feat to attempt to educate girls in the ‘whys and hows’ of science. This really shows to what extent that century took a step back from the previous one, where educational reform for women was rife, and where Mary Wollstonecraft argued that women should be educated like men.
The last chapter of part III, which concerns ‘formal education’ (grammar, Latin, Greek, science) is dedicated to logic and philosophy.
And here is more information about the author, Amyra Phelps.
Thanks to David Marans for sending me the link.