What follows below is a (slightly modified) copy of the Introduction contained in my first volume of chiastic quotes ebook, titled: Cry Chiasmus ... and let loose the blogs of words! that you can acquire - free! - at my brother site, Roger's Reference.
So, yeah, I cheated a bit to 'produce' this page. But ... no point in reinventing the wheel.
Like myself, you've seen it often: the situation in language where two or more words are used in different senses within two phrases which are, in turn, within the same sentence.
Moreover, the positioning of the words must be in reverse order, when comparing both phrases.
A very easy and well-known example is from Cicero, an ancient Roman senator. He is the first recorded to say: "I eat to live, not live to eat." For many years, when I first said that to somebody long ago, I thought that I had been the progenitor of that particular bon mot. Such is the arrogance of youth! Only much later, did I find out that Cicero had beaten me by 2000 years or more.
I could modify that quote of Cicero's very easily by saying this: "I drink to live, not live to drink!" but that's just a common, slavish copy. Yet, at another level, the statement means something very different to Cicero's dictum. Though, the best example of that construction I've ever seen is this: I just die to live, not live just to die! (That came from my youngest daugther. I wish I'd thought of it.)
Chiasmus has a long history, appearing in many languages and going back well over 2000 years, perhaps much longer. So, there is a lot to learn, and a lot from whom to learn. And, one of the first and best places to start is at Dr. Mardy Grothe's website.
Briefly though, you'll find there are a number of types of chiasmus, with implied chiasmus and double-chiasmus being just two. From my own experience over the last twenty years, it's clear to me that just about any topic can be treated chiastically--it's simply a matter of finding the right mix of words.
Fortunately, I've inadvertently helped myself to find those mixes because I've realized my fascination and foibles with homophones and homonyms, over the previous 20 years, fit quite nicely with the whole concept of chiasmus.
In truth, homophones and homonyms are the backbone of good - even great - chiasmus.
You can download all three volumes for free, anytime, at that site. Go for 'em.
Roger J Burke