How we cite our quotes: (chapter.paragraph)
Quote #7
Ron also started teaching Harry wizard chess. This was exactly like Muggle chess except that the figures were alive, which made it a lot like directing troops in battle. (12.45)
This is just a small example of how the wizarding world is filled with magic, down to the board games children play. Even the small playing pieces are "alive." When you consider how a single "live" children's toy is often the inspiration for a whole book (see The Velveteen Rabbit, The Indian in the Cupboard, The Return of the Twelves, etc.), it's pretty amazing that the Harry Potter series is so rich and full of detail that this abundant topic becomes another small detail in the magic tapestry Rowling paints.
Quote #8
'I don't need a cloak to become invisible,' said Dumbledore gently. 'Now, can you think what the Mirror of Erised shows us all?' (12.189)
In case we needed any reminding about just how powerful Dumbledore is, he tells Harry that he doesn't "need a cloak to become invisible." Harry depends on an object with its own magical properties – he or anyone else could use it with the same effects. Not so for Dumbledore's invisibility: this is magic the first-year students can't even dream of.
Quote #9
The ancient study of alchemy is concerned with making the Sorcerer's Stone, a legendary substance with astonishing powers. The stone will transform any metal into pure gold. It also produces the Elixir of Life, which will make the drinker immortal. (13.50)
This quotation from a book Hermione gets from the Hogwarts library doesn't say anything that different from what a Muggle book about alchemy might say. The philosophical study of alchemy, after all, can also be thought of as a science. The difference is that, in the magic world, phrases like "will transform… into gold" and "will make the drinker immortal" aren't just "legendary"; it really works.