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This page takes a quick look at Ancient Roman Maps - it is easy to imagine that the relatively recent discovery of new territories, the lack of bird's eye views and of precise quantity surveying instrumentation would mean that the maps drawn up by the ancient Romans were extremely distorted.
This perception of ancient roman maps should be counterbalanced with the astonishing accuracy with which aqueducts were built, which in itself gives us an idea of how skilled the Romans were in utilising their basic surveying equipment: The inclination of the aqueduct had to be carefully measured and maintained, according to Pliny 1ft in 4800 and this would even have to vary along the course of the aqueduct in accordance with the type of construction technique, in order to jump small heights or make use of siphon effects.
We have the general idea that the chosen route of construction would be a straight line but clearly if a straight line meant tunneling excessively tough rock, crossing very deep valleys or, most importantly, building an aqueduct with an excessively steep gradient then the aqueduct would have to be made longer by introducing bends which might follow valley sides and hills and allow the necessary length for the adequate gradient to be achieved. We can see that this required an extremely precise understanding of topography, at least at local scale!
Another surprising contradiction to distorted maps is provided by Roman roads: Roman roads were notably (quite) straight and the network was also extensive throughout the empire and relatively well measured out. You would think that by taking a map of the road network with the mileage points, combining that with your local topographical knowledge and knowledge gained in the construction of aqueducts you should be able to interpolate (or extrapolate?) a relatively good approximation to reality. Perhaps that's what Agrippa's map did and why it took 20years to compile....
The Romans had adopted a concept of the world from the Greeks who suggested it was a sphere situated at the centre of the heavens which themselves were a sphere of stars. This had great significance in a variety of fields ranging from navigation and map making through to religion and astrology. This basic understanding of the heavens would have been essential in terms of defining general orientation and direction. eg it would be quite evident to someone navigating or travelling along the south coast of France (Gaul) that they were traveling east-west etc. The sphere came to be a symbol of power symbolising rule over the world.
Proper topography (and map making) would require you to measure orientation/angles and height as well a distance. Great engineering works such as tunneling (where tunnels are started at both ends and made to magically meet in the middle) and aqueducts demonstrate that the basic instruments such as the goniometer the "groma" and "coriobate" permitted great levels of precision. These tools were frequently used by the "agrimensor" to precisely subdivide farmland, ie they were quite commonly available. If I'm not wrong a tablet found in Pompeii actually signposts some chap's instrumentation shop.
As far as distances are concerned the Romans made good use of the odometer: basically a simple cart with wheels which drove a shaft round which in turn drove a counter, for example every full turn of the vertical shaft might release a pebble into a bin.
So back to Ancient Roman Maps, I don't know of any surviving ancient Roman topography maps, such as might have been drawn to design and build the 400km or so of aqueducts across the empire, but we do have some surviving testimony of large scale maps and these give us a suggestion of how the Ancient Romans might have viewed their own world. These Roman maps are as initially expected quite distorted, in spite of the great orienteering and topographical ability observed in engineering works.
So was the distortion driven by ignorance or need? The answer lies somewhere in the middle: The maps were actually pretty amazing and at the same time the Romans were extremely practical. Unlike the Greeks, who might have spent great effort in achieving true scientific knowledge the Romans preferred to save their efforts up for material necessity. And so the large scale maps could be left distorted or purposely exaggerated in order to convey precise meaning with relatively accurate road and place markings on them.
Map making was one of those areas bordering between resource hungry science and material necessity, particularly to a people who's wealth relied on military and commercial control across vast territories. Maps had to be good to consolidate that military and commercial superiority.
Map making received a special impulse during the age of Caesar and Augustus. During the reign of Augustus a complete map of the empire was drawn up and came to be known as "Agrippa's map" (Agrippa was Augustus' right hand man). Completion of the map took a full 20 years of work. Shame I haven't a copy to hand, it must have been brilliant.
Just like a modern metro map, Ancient Roman Maps might squeeze distances onto a straight line which got you from A to B in a more or less expected period of time and told you which stops are along the way. It is quite likely that a great deal of distortion was actually done on purpose so that the map could convey the information required as succinctly as possible.
A particularly good illustration of this can be had from the famous "Tabula Peutingeriana" which is a (unique) medieval copy of an ancient Roman map. The map's name derives from its last owner a Mr. Konrad Peutinger who obtained it at the beginning of the 16th century. Although the map is clearly a medieval copy of some Roman original it is difficult to establish exactly when the original might have dated to since it includes places such as Pompeii, Herculaneum and Stabiae which were "deleted" from the face of the earth when Vesuvius erupted in 79AD. On the other hand there are places shown with their late Empire name and indeed Gaul is called with its even later name of France! The map is a long scroll measuring 682cm x 34cm (the romans used scrolls of parchment rather than books), quite long.
This mother of all Ancient Roman Maps was probably meant to be used by Imperial messengers who used all major routes of the empire. It greatly deforms "actual" geographic profiles so that the most important parts of the empire can be displayed in the 34cm of height. You couldn't really make it much taller than those 34cm or it would have become a bit cumbersome as a portable road map!
For example, Italy is laid on its side just above a strip of water with islands and then Africa across the bottom. The rest of Europe is squeezed across the top so that the Balkans, for example, are shown as a strip across the top, divided from southern Italy by a strip of water. The Aegean, its islands and Greece are shown further to the right, ie below Italy's heel, and fit into their proper place connected to Macedonia to the north and separated from north Africa by a strip of water.
Mountain chains are fitted into their relative locations for example the Atlas mountains define the bottom edge of the scroll. Cities, major and secondary stopping and resting points (our equivalent of petrol stations and hotels), tunnels, bridges, thermal baths, temples and so on are all carefully shown. In total there are something like 500 to 600 symbols on the map.
This section of map shows Rome at the centre with 12 major roads fanning out in the different directions. Each of the roads is labeled with its name eg first at bottom left is the Via Aurelia followed by the Via Triumphalis, Flaminia, Salaria and so on. The edifice shown under Rome (but actually to its West, given that Italy is laid sideways) is the port of Ostia, one of the main trading routes onto the Mediterranean which regularly received Rome's food and commercial supplies from across the Empire.
Throughout this ancient AA road map, the roads themselves aren't always shown as straight lines connecting two given localities: they could be drawn as stepped or snaking to destination, conveying an improved sense of road distance as well as keeping the map neat and legible with roads running parallel to the map's layout.
This wonderful map also shows us that some northern areas were measured in Leagues rather than Miles!
As has already been mentioned distances could be measured out relatively accurately using an odometer. What we might not immediately realise is how useful it is to have a standardised measure of distance. Even in ancient roman times standardisation was not quite fully and properly achieved (some areas of the northern empire used Leagues rather than miles). Lyon northwards (Narbo) was where leagues were used: "usque hic leguas".
Ancient Roman measures of distance:
Measures of area (eg for agricultural purposes):
As an interesting but completely useless aside I remember reading that our modern roads conform in width to old standards which were set for horse and carriage transport, which themselves were set by the Romans (based on the average width of a horses' behind). Now, given that the space shuttle was designed to fit through the tightest tunnels it might have to be transported through we can conclude that.... Useless information, I admit, but it sounds credible.
Other notable elements of testimony date to around the third and fourth centuries AD: The "Itinerarium Burdigalense sive Hierosolymitanum" gives a detailed account of the route between Bordeaux and Arles. It dates to about 333AD.
The "Itinerarium Antonini Augusti" has no map but provides a detailed description of roads and routes in the empire. It seems to date back to the age of Emperor Caracalla ie around 215AD.