You most likely subscribe to a progressive view of history as a whole, meaning that society advances linearly (populations become more civilized, more knowledgeable, more advanced, etc, essentially superior to those in the past).
You most likely believe (implicitly or explicitly) the purpose of history is to define and bolster the nation state, to define the pedigree and accomplishments of the nation in a way which promotes patriotism and loyalty. There is most likely an element of racial or geographic bias to this, meaning a promotion of white, western European perspectives over others.
You most likely hold a Rankean view of history, which is to say you believe there are inherent historical facts and truths which can be uncovered and described. This means you view historical interpretation as objective rather than subjective.
You most likely ignore historical perspectives which aren't "top down." You look at important government officials and other rich white men, and are not concerned with the experiences of women, people of color, working class people, etc.
Would a historian back then also have huge differences from us in terms of what archaeological data he had? I know technology played a big role in terms of our gaining raw data about ancient history, but I don't know what was discovered then. How big would the gap between our understanding of ancient cultures and the 1900 historian's be?
Can I ask a follow up? How does this change depending on which country you live in. I partially suspect that there might be differences between the west (UK/Germany/France/US) and the east (China/Japan), but I recognize that colonialism may have westernized the east quite a bit by that time.
Also, at what point did a progressive view of history become the norm (here I'm riffing off /u/Borimi's answer? How far back would one need to go to get a different view of history?
In a different vein, if you are like me, and interested in what people believed in the past that we would disagree with today, you may try looking at an encyclopedia, or a collection of books from the time period you're curious about. I have a rather interesting/discomfiting compendium from 1902, "Triumphs of Our Era" edited by Trumbull White which contains, in particular, Book III: "Marvelous Peculiarities and Noteworthy Facts of All Nations and Countries of the World" and Book V: "Things We All Should Know."
I don't know enough about compendiums to suggest that they were collections of asserted facts, but it appears that the statements contained within are at least thought to be true. If nothing else, this book provides an interesting look at the attitudes of the author(s) towards different peoples, and what they considered to be useful knowledge.
If you are a historian in the US, depending on where you were educated (North or South) you have a very different view of the central issues of the Civil War. Most Northern historians at the time viewed the war's central issue as the abolition of slavery (in reality, at the opening of the war, most Northerners fought for the preservation of the Union, later, after the Emancipation Proclamation added the end of slavery as a war goal). Southern historians on the other hand completely dismissed the role of slavery as a central issue of the war (unlike the North, the central issue from the get go was the preservation of slavery, Southern historians at the time argued that it was about "states rights" although the only right that Southern states had that Northern states did not was the ability to own slaves).
Although the war itself had been settled, Northern and Southern historians continued to fight over the different interpretations of the causes of the war.
Frank Lawrence Owsley was one of these Southern historians at Vanderbilt University. He was mainly educated in the South, but did his Ph.D. in Chicago. Owsley was a member of the Southern Agrarians at Vanderbilt that promoted a very pro-Southern and socially conservative image of the South. He was a smart guy and made some sound interpretations (mainly the influence of the average Southerner on the community), but his states rights arguments are very outdated.