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I would use respectively in either one of the following ways:

"Figures 1 to 3 are respectively front, top and bottom views of the object",

"Figures 1 to 3 are front, top and bottom views of the object respectively"

(with a strong preference for the former).

But I am presented it as:

"Figures 1 to 3 respectively are front, top and bottom views of the object".

Is the later form a more formal (such as when used in official documents, patents, literature) use of respectively or is it incorrect?

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Using respectively at the end of the sentence is the normal structure:
"Figures 1 to 3 are front, top and bottom views of the object, respectively."

However, respectively can be placed parenthetically in the middle of the sentence as in the other two forms. All are acceptable. Note, however, that a parenthetical needs to be separated by commas on both sides:
"Figures 1 to 3 are, respectively, front, top and bottom views of the object."
"Figures 1 to 3, respectively, are front, top and bottom views of the object."

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    To add to this, some internal style guides require "Figures 1, 2 and 3" to make the list explicit and to emphasize the one-to-one pairing imparted by "respectively." – Chemomechanics Feb 21 '18 at 18:09
  • @Kris: are both commas mandatory on both sides of the parenthetical? It seems to me that the commas would add some unnecessary heaviness (or slowness upon reading due to an over-emphasis on "respectively") to what is otherwise a short and straightforward sentence. I would see them as optional. – calocedrus Feb 22 '18 at 5:49
  • @Chemomechanics given the enumerative nature of respectively, I'd agree with you internal style guides. – calocedrus Feb 22 '18 at 5:49
  • OP, yes, a parenthetical should necessarily be separated by commas. Sometimes a dash may be used instead. The reason is that a parenthetical expression interrupts the sentence structure - try reading the sentence without the expression: it is still grammatical, makes sense and is complete on its own. HTH. – Kris Feb 22 '18 at 10:18
  • @Kris: is respectively, as used in the 1st and 3rd form in my question, a parenthetical? Does the fact that it "can be placed parenthetically" (as you wrote in your answer) make it necessarily parenthetical? I would tend to think that that "respectively" in the forms 1 and 3 may or may not be considered parenthetical. Well, I think that could be the subject of questions about parenthetical ... A side note: it seems "parenthetical" is an adjective, not a noun. – calocedrus Feb 23 '18 at 8:42

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