And are there special names for each of the four sides? If so, what are they?
I may wish to ask my typesetter to indicate the imaginary line between the margins and the body text with a red outline.
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Ask your typesetter to outline the type area for you. The English term is a bit ambiguous here, in German for instance the somewhat more precise term is "Satzspiegel".
To give you a bit of context:
A big decision in editorial design is to decide where to place content on the page/spread. Here's a very traditional/simple way of defining this placement:
Note, that they are different for top/bottom inside and outside – to accommodate binding or pagination for example.
It is simply the "Margin" (Top Margin, Bottom Margin, Left Margin, Right Margin).
The Margin is the invisible line and not something you can color or even delineate. (beyond not having your subject material spill into it).
In Adobe Illustrator you would create a text box (to the Margins) for your text and add a red stroke to the text box.
To be able to convey this to your typesetter something along the lines of:
"I want a 2 point wide red box around the type, at the margin, with the type inset 3 points inside the box."
Depending on the program your typesetter is using there will be (should be) different ways to do this.
In Adobe inDesign and other page layout programs, those lines are called guides. There are margin guides, column guides, bleed guides, and slug guides. The guides are non-printing "imaginary" boundary indicators. You can toggle between "show guides" and "hide guides."
The margins themselves comprise the area between the edges of the page and the area where the printed matter appears—the "live area."
What I think you want to tell your typesetter is: Please delineate the live area. Or—if you're speaking plain English: Please draw a line around the live area.
It's always interesting when linguistic people communicate with visual people. I often learn from it. This is a good example of how writers and designers sometimes talk past each other. Linguistic people tend to be very precise when describing visual things. Sometimes to a degree where it actually confuses visual people who, on the other hand, can be quite sloppy with their language.
When you want the designer to "indicate the imaginary line between the margins and the body text with a red outline" you are being very precise. Simply asking the designer to "indicate the margins with a red outline" should suffice.
Similarly you wouldn't ask for someone to "outline the imaginary line between the area inside the rectangle and the area outside the rectangle". You would simply ask them to "outline the rectangle".
These are layout margins (bottom, top, left, right)
Layout margins provide a visual buffer between a view’s content and any content outside of the view’s bounds. The layout margins consist of inset values for each edge (top, bottom, leading, and trailing) of the view. These inset values create a space between the edges of the view’s bounds rectangle and the content inside the view.
They may also be referred to as inset spacings
There's no particular word for it, as far as I know. They're just edges of “text block” or “type area”.
I'd ask them to outline the text block or type area edges, or to make a bounding box around them.
Robert Bringhurst, The Elements of Typographic Style:
Textblock: The part of the page normally occupied by text.
James Felici, The Complete Manual of Typography:
Type area: The part of a page populated by the main text and usually defined by the top, bottom, outside, and binding margins.
Ellen Lupton, Thinking with Type:
“Hanging punctuation” prevents quotations and other marks from taking a bite out of the crisp left edge of a text block. [...] Make a clean edge by pushing the quotation marks into the margin.
Justified text, which has even edges on both the left and right sides of the column, has been the norm since the invention of printing with movable type, which enabled the creation of page after page of straight-edged columns.
Erik Spiekermann, Stop Stealing Sheep & Find Out How Type Works:
To achieve a nice, smooth edge on both sides of the column, the punctuation is hung in the right hand margin.