Hah! Same here, but with me, it’s always “The old Koob”.
Make sure you don’t sneeze while saying the incantation…
You are aware of the existence (uh…) of succubi and incubi, who are basically booty-demons, right?
Firstly I want to be on the same side of the pentacle as Willow and Anya. 
Next I refer to my sources:
‘The Devil rides out’ (film + book by Dennis Wheatley) … stand inside the circle for protection
'DiscWorld … stand outside the circle for protection when Death is summoned (by the Rite of Ashkenzy)
OK, I got nothing. 
First you need to determine whether the demon you are invoking is already loosed upon the face of the Earth. If it is, you stand within the enchanted circle. You are just bringing a co-dimensional entity into close physical proximity, and the circle will act to keep that entity from eating your mind before you can slap a geas on it.
If the being you are summoning in currently on one of the Other Planes, then the circle will act as a containment system for that entity and prevent it from ravaging this plane. In that case, of course, you stand without the circle and direct the demon to manifest within.
Don’t try this at home without professional consultation.
For added protection, why not draw two pentacles (pentagrams?)- one for yourself, and one for the demon?
Would that be like double bagging?
It’s AshkEnte, not Ashkenzy, you fool. (Technically, ‘Death’ should also be in small caps, but I have to find out how to do that.
On further poking around, it turns out that “Weave a circle round him thrice” is actually not from Shakespeare at all, but Coleridge’s Kubla Khan. Unfortunately, the poem is sufficiently opium-addled as to be unclear whether the narrator intends to weave the circle about a demon (possibly the incubus the woman is wailing about in the second stanza?), or the world at large will feel the need to weave the circle about the narrator, once he reveals his creative greatness. Or if possibly the two are the same.
dwalin, to properly invoke DEATH, just use the [size] tag.
Insert obligatory Convergent Series reference here.
There’s gotta be a potential for a decent T-shirt here somewhere. Maybe a large pentagram with the words: “Are you in or out?” or “you put your left leg in…”
Okay, I was, OMG, wrong!
Ep guides say his name is Abraham Benrubi. Sure looked/sounded like Goodman. I’ve been sure all these years and yet…WRONG! ugh!
I’m curious as to who has actually summoned a smitin’ demon or sexin’ demon. Book knowledge is all well and good, but “magic” lore is so polluted by popular fiction, role playing games, and outright liars that I just assume anything from the web or a corporately published book is unreliable information. So, who here has actuall had an enemy smote by a demon of their own summoning? Anybody here actually tapped some demon ass?
The OP reminds me of a classic Berni Wrightson illustration:
The scene: a pentacle, with candles smouldering at each point. In the center sits a huge, gargoyle-like demon, fresh from the pits of Hell. And splaying from underneath our heavyweight demon we see the spindly legs and arms of the flattened demon-summoner.
Wish I could find a link.
All the 20th century stories I’ve read have the wizard or summoner outside the circle, and the demon inside, but I recalled this woodcut after reading this thread, and have to admit that you’re probably right about it being originally the other way:
I wrote a story many years ago (“Device Invected”) in which the wizard reversed the positions on purpose, putting himself inside so that the demon could wreak havoc on the world outside. Interesting to see that that was the original intent.
If you want a weird take on this by a mathematically-minded sf/fantasy author (where, again, the demon goes inside the pentagram), read Larry Niven’s “Convergent Series” (In the collections The Shape of Space and, of course, Convergent Series.)
…
If you’re working with demons of the Chinese pantheon, you may want to consider double tea bagging.
I wish I’d said that! 
But, as we all know, sometimes the goggles do nothing.
Do you also have to hold your hands under your armpits and do something like an elbow flapping motion? I think that would add to the overall impression. If I were a demon, I know I’d be more likely to show up if someone were summoning me with that type of action. It’s more…compelling, somehow, ya know?
Fascinating Google ads below this thread . . .