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According to the Historical Dictionary of Science Fiction, the earliest known use of "Terran" as a noun meaning "a native or inhabitant of the planet Earth" (aka Earthian, Earthie, Earthling, Earthman, Tellurian, Terrestrial, Terrestrian, etc.) was in Astounding Science Fiction, April 1946 (available at the Internet Archive), in part 2 of the serialization of George O. Smith's novel Pattern for Conquest. The quotation is from p. 10, column 2:

The earliest citation for "Terran" as an adjective is from part 1 of the same story, in *Astounding Science Fiction, March 1946, available at the Internet Archive. The quotation is from p. 9, column 1:

However, the form "Terrane" was seen earlier, in the 1881 novel Three Hundred Years Hence by William Delisle Hay:

According to the Historical Dictionary of Science Fiction, the earliest known use of "Terran" as a noun meaning "a native or inhabitant of the planet Earth" (aka Earthian, Earthie, Earthling, Earthman, Tellurian, Terrestrial, Terrestrian, etc.) was in Astounding Science Fiction, April 1946 (available at the Internet Archive), in part 2 of the serialization of George O. Smith's novel Pattern for Conquest. The quotation is from p. 10, column 2:

The earliest citation for "Terran" as an adjective is from part 1 of the same story, in *Astounding Science Fiction, March 1946, available at the Internet Archive. The quotation is from p. 9, column 1:

However, the form "Terrane" was seen earlier, in the 1881 novel Three Hundred Years Hence by William Delisle Hay:

According to the Historical Dictionary of Science Fiction, the earliest known use of "Terran" as a noun meaning "a native or inhabitant of the planet Earth" (aka Earthian, Earthie, Earthling, Earthman, Tellurian, Terrestrial, Terrestrian, etc.) was in Astounding Science-Fiction, May 1946 (available at the Internet Archive), in part 3 of the serialization of George O. Smith's novel Pattern for Conquest:

The mission, not entirely understood by the Terrans, consists of destroying a machine sent forth by the Loard-vogh, a race that is conquering the Galaxy on a twenty-thousand-year program. This machine restricts mental activity through a vast area, thus permitting the Loard-vogh to advance without difficulty. Communication between the Little People of Tlembo and Terrans is also restricted by the machine, and so the true nature of the mission is not really known.

The earliest citation for "Terran" as an adjective is from the same 1946 George O. Smith story:

"Seventeen million of the Loard-vogh died in the Battle of Sol, and more than half of them perished because Terran spores crept into chinks in their space armor. Chinks so small that they do not permit loss of air in space.

The earliest citation for "Terra" as a name for the planet Earth is from an 1871 lecture "Science & Revelation" by Robert Payne Smith:

Jeff Prucher, an associate of the Science Fiction Citations site, wrote the following essay on "Earthlings" in his Hugo-winning book Brave New Words: The Oxford Dictionary of Science Fiction:

In science fiction, when beings from different worlds encounter each other, they are generally named by their planet or star of origin; thus Martians are from Mars, and Sirians are from some hypothetical planet orbiting the star Sirius. While there are generally few terms in use for beings from any given planet or solar system, there is much greater variety in the terms for people who are from Earth. Many of these terms have been in use for centuries in other senses. Some, such as Earthling and Terrestrial, originally designated earthly (as opposed to heavenly or spiritual) beings. Terrestrian was once an adjective used to describe animals that lived on land rather than in water. Earth-man and -woman once referred only to beings that were associated with soil or the ground in some way; once SF writers got hold of them, they added Earth-folk, Earth-girl, and Earth-person as variations. SF writers also coined the fairly common terms Terran, Tellurian (after Tellus, the Roman goddess of the earth), Earther, Earthian, and Earthie, in addition to many more that never quite caught on, including Earthan, Terrene, and Terrestial. However, when faced with creatures from another star system entirely, beings from the Moon or Jupiter may seem slightly less alien, and so the word Solarian was coined to refer to any inhabitant of Earth's solar system, human or otherwise—Earthling, Martian, and Plutonian alike.

Update. Here is an earlier (by one month) citation for "Terran" as a noun, from part 2 of the searialization of George. O. Smith's Pattern for Conquest, in Astounding Science Fiction, April 1946, available at the Internet Archive. The quotation is from p. 10, column 2:

Neckal spoke: "The battle progresses."

Vorgan frowned. "Why or how can one so small defend himself against one of the Planet of Terror?"

"The Little Man is agile and the Terran is clumsy."

Lindoo nodded. "We may both curse and praise that. If the Terran were less clumsy, he might well be more difficult for Kregar."

There are still earlier citations for "Terran" as an adjective in part 1 of the same serial, in Astounding Science Fiction, March 1946, also available at the Internet Archive. This quotation is from p. 9, column 1:

Stellor Downing was Martian by birth and by six hundred years of Martian-born forebears. His family could trace its line back to the first group of Terran colonists that braved the rigors of Martian life before technology created a Martian world that was reasonably well adapted for human life.

According to the Historical Dictionary of Science Fiction, the earliest known use of "Terran" as a noun meaning "a native or inhabitant of the planet Earth" (aka Earthian, Earthie, Earthling, Earthman, Tellurian, Terrestrial, Terrestrian, etc.) was in Astounding Science Fiction, April 1946 (available at the Internet Archive), in part 2 of the serialization of George O. Smith's novel Pattern for Conquest. The quotation is from p. 10, column 2:

Neckal spoke: "The battle progresses."

Vorgan frowned. "Why or how can one so small defend himself against one of the Planet of Terror?"

"The Little Man is agile and the Terran is clumsy."

Lindoo nodded. "We may both curse and praise that. If the Terran were less clumsy, he might well be more difficult for Kregar."

The earliest citation for "Terran" as an adjective is from part 1 of the same story, in *Astounding Science Fiction, March 1946, available at the Internet Archive. The quotation is from p. 9, column 1:

Stellor Downing was Martian by birth and by six hundred years of Martian-born forebears. His family could trace its line back to the first group of Terran colonists that braved the rigors of Martian life before technology created a Martian world that was reasonably well adapted for human life.

The earliest citation for "Terra" as a name for the planet Earth is from an 1871 lecture "Science & Revelation" by Robert Payne Smith:

Jeff Prucher, an associate of the Science Fiction Citations site (precursor to the Historical Dictionary of Science Fiction), wrote the following essay on "Earthlings" in his Hugo-winning book Brave New Words: The Oxford Dictionary of Science Fiction:

In science fiction, when beings from different worlds encounter each other, they are generally named by their planet or star of origin; thus Martians are from Mars, and Sirians are from some hypothetical planet orbiting the star Sirius. While there are generally few terms in use for beings from any given planet or solar system, there is much greater variety in the terms for people who are from Earth. Many of these terms have been in use for centuries in other senses. Some, such as Earthling and Terrestrial, originally designated earthly (as opposed to heavenly or spiritual) beings. Terrestrian was once an adjective used to describe animals that lived on land rather than in water. Earth-man and -woman once referred only to beings that were associated with soil or the ground in some way; once SF writers got hold of them, they added Earth-folk, Earth-girl, and Earth-person as variations. SF writers also coined the fairly common terms Terran, Tellurian (after Tellus, the Roman goddess of the earth), Earther, Earthian, and Earthie, in addition to many more that never quite caught on, including Earthan, Terrene, and Terrestial. However, when faced with creatures from another star system entirely, beings from the Moon or Jupiter may seem slightly less alien, and so the word Solarian was coined to refer to any inhabitant of Earth's solar system, human or otherwise—Earthling, Martian, and Plutonian alike.

According to the Science Fiction Citations site, the earliest known use of "Terran" as a noun meaning "an inhabitant of the planet Earth" (aka Earthian, Earthie, Earthling, Earthman, Tellurian, Terrestrial, Terrestrian, etc.) was in Astounding Science-Fiction, May 1946 (available at the Internet Archive), in part 3 of the serialization of George O. Smith's novel Pattern for Conquest:

According to the Historical Dictionary of Science Fiction, the earliest known use of "Terran" as a noun meaning "a native or inhabitant of the planet Earth" (aka Earthian, Earthie, Earthling, Earthman, Tellurian, Terrestrial, Terrestrian, etc.) was in Astounding Science-Fiction, May 1946 (available at the Internet Archive), in part 3 of the serialization of George O. Smith's novel Pattern for Conquest: