I may be over-pernickety, but I am inclined to approach a work where the title purports to be The History of [Whatever] with caution.
A History of [Something] is acceptable. Change the article at the front to something more definite, and there's more than a hint of hubris.
Your dictionary's definition of history 1 will present various possible meanings to accompany the different senses of the word.
Take the branch of knowledge that deals with past events and stretch it back to wherever that past begins; that's a vast array of incidents and individuals.
So, The History of North Queensland or The History of Australian Exploration is acceptable as a specialist topic in a quiz programme.
In that sense, one accepts the possibility that there are gaps in the participant's knowledge.
The point of the exercise is to match knowledge against an external benchmark.
Call your book The History of Australian Exploration, and you suggest that it's all there under a single roof. If you change the title to A History, you acknowledge that you have been selective.
When writing history, one starts by filtering out anything that seems irrelevant to the narrative one is looking to advance.
So a history of world exploration will almost certainly mention Marco Polo, Henry the Navigator, Bartholomeu Diaz, Vasco da Gama, Christopher Columbus, and Ferdinand Magellan.
However, one can safely leave them out of an account that deals with Australia.
Or can you?
If you limit your scope to figures who encountered the Australian coastline, none of them will figure in your account.
On the other hand, if you want to examine the factors that brought European travellers to Australian shores, all may rate a mention.
It all depends on the narrative an author wants to weave.
So let's start with Marco Polo, acknowledging that he never reached Australia.
However, his return journey after his lengthy sojourn in the Orient brought him relatively close to Australia.
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1 So, in the Shorter Oxford Dictionary (abridged):
history noun.
1 A narration of (in later use, esp. professedly true) incidents; a narrative, a story. Obsolete except as passing into sense 2.
2 spec. The continuous, methodical record of important or public events, esp. those connected with a particular country, individual, etc.
3 The branch of knowledge that deals with past events; the formal record or study of past events, esp. human affairs. Frequently with specifying word. economic history, French history, Marxist history, medieval history, modern history, social history, etc.
4 Orig., a story represented dramatically. Later, a historical play.
5 A story represented pictorially; a historical picture.
6 A systematic account of natural phenomena etc. Now chiefly in natural history
7 a A series of events (of which the story has been or might be told).
b The whole train of events connected with a nation, person, thing, etc.; an eventful past career.
c The aggregate of past events; the course of human affairs.
ORIGIN: Latin historia from Greek = learning or knowing by enquiry, narrative, history, from histōr learned, wise man, ult. from Indo-European base also of wit verb.