The spelling of the word "Sagathy" is not a commonly used term, and it may be confusing to figure out how to pronounce it properly. However, using the International Phonetic Alphabet (IPA) transcription, we can break it down. The IPA transcription of "Sagathy" is /səˈɡæθi/. This indicates that the word is pronounced with the first syllable being unstressed ("sə"), followed by a stressed "gath" sound (which rhymes with "math"), and ending with an "ee" sound at the end (/i/).
A mixed fabric of silk and cotton; a kind of serge.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.