You are sending a link to...
Apophthegm not apothegm
I’m sticking to my guns on this. Of course you don’t need to put the –ph- in, as it is not pronounced, but reason not the need. Basest beggars can choose an extra letter or two. Apophthegm is much more fun than apothegm. Apothegm is for Roundheads, but apophthegm is for Cavaliers.
Besides, if we start leaving letters out merely because we don’t say them, where will it end? Would you spell Cholmondesly-Featherstonehaugh as Chumley-Fanshaw? Or leave out the letter “u”, making words colourless and flavourless?
And, what about the other way round? Do we have to pronounce the silent “t” in Harlot?