We usually use “on page” because we think of a page as a surface. We use the preposition of place “on” with surfaces in English. We don’t usually use “in page” but it can be used when something appears within the page. We use “at page” when we need to use the page as a reference point.
The story continues on page 15.
Where are you in the book? I am at page 23.
“On” in this case is a “preposition of place”. That means that “on” helps us to understand the location in relation to the noun(in this case “page”.
We use “on” with surfaces as it shows the relative position of something. Think about an easy example: “the cup is on the table”. The position of the cup is supported by the table.
The word “page” usually supports the text and for that reason, we use “on”.
The report starts on page 3 and finishes on page 15.
Where is the photo? It is on page 54.
We also use “on” for webpages as we treat all technology with screens as surfaces. Everything on the internet like websites, apps, and platforms will use the preposition “on”.
I sent him a message on Facebook.
You can see a picture of me on the homepage.
“On-page” is a type of Search Engine Optimization where people focus on the content written on the webpage and not on other factors like links(off-page).
“In page” is not very common in English as we use the preposition of place “in” with volumes. If you said “in page”, it would probably mean something like within the physical boundaries of the page like in the margins of the page.
“In” is used for things that have something within them like “chapters” and “books”.
The thematic conclusion is in chapter 17.
I can’t find an explanation in my book.
We use the preposition “at” when we want to show that we are at a relative position. When we use the word address(either physical or digital), we often want to use it as a reference point so other people can know where we are.
We use “at page” when we want to show a location of a page in the book.
The funny part starts at page 15.
I stopped reading at page 23.
You can also use “on” in the above examples:
The funny part starts on page 15.
I stopped reading on page 23.
Open your books To or On Page
Both “open your books to page” and “open your books on page” are correct.
“Open your books to page” is more common in American English and “open your books on page” is common in British English.
It is important to note that even though some other possibilities exist, in the vast majority of cases “on” is the most likely proposition you will need with “page”.