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Sorry if I didn't understand exactly what you mean, but:

When you take the rectangular selection tool and select your first "element",

 then, whilst holding shift select your second, third etc untill you have selected all you want to print

Ctrl/Cmd + C to copy the selection to the clipboard

Ctrl/Cmd + V to paste it unto a new layer

uncheck all the eye icons except the one of the layer with the selection so that only that one is visible

and then choose Print with preview

you only print what you selected.

Is it this you are looking for?