How do lines of longitude differ from lines of latitude?

In many ways.
All lines of Longitude are Great Circle lines, which means that, coupled with their opposite one (Latitude 75° and Latitude 255° for example) they form a great circle around the Earth whose radius is constant.
Latitudes are not Great Circles, except for the Equator. The circle their section represents on the Earth becomes smaller and smaller as you cut nearer to the two poles.
Latitudes have a natural reference point (the Equator is 0° Latitude) and two natural ends (the two poles at plus or minus 90°).
Longitudes, because they are all equal, have a man devised reference point (the meridian going through the Observatory of Greenwich near London).
You might be interested in knowing that a dispute about the longitudinal reference point is the reason why they speak Portuguese in Brazil and Spanish in the rest of Latin America.
Finally, you can determine your Latitude by sighting the , but you cannot do it for Longitudes. For that you need a reference time (Greenwich) and an accurate timepiece.

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