A lesson in surveying.
In the 80's I attended a school that specialized in land surveying. I was in a different course but living in a house with surveyors for a year I got to know a little about the science behind it as you spent time chatting about what you are doing.
There are two types of surveying: plane surveying and geodetic surveying.
Plane surveying is used for areas up to about a hundred square miles and for projects that are primarily linear. Geodetic surveying is used once the project area exceeds about a hundred square miles and when exact precision is needed.
Plane surveying doesn't explicitly account for curvature of the Earth's surface while geodetic does. Plane surveying is the most common since most projects are small and level is the primary concern over spatial accuracy. It's also simpler and allows for simpler equipment. The curvature of the Earth is inherently accounted for in plane surveying by the technique used in leveling point to point, visualized and explained here:
http://ecoursesonline.iasri.res.in/mod/page/view.php?id=128291
The technique has limitations but allows the surveyors to consider the area 'flat'.
The key is to mark level by positioning the leveling scope exactly midway between the points and not from one of the points. You'll see how it's done in the link above. If you simply marked level from one point the next, it wouldn't work because you would gradually rise upwards from 'level' because you would be progressing in a tangent from the starting point. By marking level from in between the two points, each segment connects to the previous one at a very slight angle that progressively follows the curve of the Earth and avoids the tangent. This is why plane surveying, the most common form used, doesn't require accommodating the curve of Earth since the technique takes care of it for you.
Geodetic surveying is truly spatial and necessary once large areas of land need to be surveyed since accumulated areas become impossible to reconcile. Geodetic is rooted in math and physics since precision is the key requirement.