Stonehenge was built on solstice axis, dig confirms

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15. Most Aquaducts were and are ground level

The oldest Roman Aqueduct is actually underground and still in use. Using ground and water flow is sufficient to determine drop. You do NOT need to do any math is such a simple system. Enlarging the system only require a deeper ditch and more water from the source.

Now you do need to know extensive math and calculations when building the stone structures most people think of when you think of Aqueducts. I even mentioned that. and then pointed out most such structures were uniform height and the water flow adjusted at the top.

Plumb bobs

When these routes were surveyed, all they had was basically a stick of a set height and a plumb bob. The Plumb bob could be attached to a line and when the other side of the line caused the plumb bob to be at a notch in the center of the base, the line was level. Very simple, very ancient, very accurate.

Now a modern water level is more accurate, for a modern level has its water encased in a sealed tube with one air bubble. When the air bubble inside is between the two marks on the bubble. Very accurate, but only really needed is you want to build over hundreds of miles with curves. The Aqueducts tended to avoid curves (They had them, but it was avoided if it could be done).

A plumb bob is still used, through it is considered more fashionable to used more modern methods (i.e. Modern levels tend to be more accurate, but in most construction other errors exceed the greater accuracy of modern equipment over Plumb bobs). A plumb bob is a simple device, it is generally attached to a flat top (to attach to a line) and triangle bottom. A weight attached to the middle of the top by a short string. When the string meet the mark at the bottom of the device, you knew you were level. Very simple, very effective and accurate:

http://en.wikipedia.org/wiki/Plumb_bob

Here is a drawing on the evolution of the Dioptra, the one further to the left is a Plumb Bob, the other two are Dioptra, used mostly in construction. No Records of them in Rome, but were known to the Greeks. This may be simply the result that they had become so common, no one wanted to waste parchment (Which was expensive) on writing about them. An alternative answer was the Romans did not think it was that much of an improvement over the Plumb bob, something the builders of the great Cathentials during the Middle Ages would have agreed with.



Variation of the Plumb Bob was used through out history, the Ancient Greeks used the Dioptra:

http://en.wikipedia.org/wiki/Dioptra

Another Greek variation of the Plumb Bob, The Groma:

http://en.wikipedia.org/wiki/Groma_surveying

More on Roman Engineering:

http://www.surveyhistory.org/ferris_state_university1.htm

In many ways, the key to Roman Engineering was getting the people together to do the work NOT in the calculations.

On the other hand, with a line and a plumb bob you could survey a flat route with ease, and whenever you wanted a drop, drop the line. If you wanted a drop off 1 inch every 100 feet, every 100 feet you move the line down one inch. When the actual construction was done, the workers using water would make the final adjustment.

Lead pipes

As to fountains within the City of Rome. That is based on the concept that water will find its own level. Thus if the water flowing into Rome is at a higher attitude then any fountain or other water source in Rome (or any other city) AND the flowing into a system that is sealed (i.e. enclosed pipes NOT open water ways, the Aqueducts were mostly open water ways, except when it was decided to use pipes). Thus you do not have to known how low or high the pipe is, just that it is below the intake to the water system as a whole. Modern plumbing follows the same rule.

Pipes, made of lead, were extensive in Rome itself AND on various Aqueducts when it was determined the best way to transport the water was down one mountainside, along the valley in a sealed pipe made of lead, then up another Mountain. In such situations all you had to do was make sure the pipe was SEALED and the end closer to Rome was lower then the end further from Rome (at one time this extensive use of lead was blamed for Rome going "Mad" and leading to its decline, but the water in that part of Italy is extremely "Hard" and as such pick up little lead as it flows through the Roman Pipes).

http://penelope.uchicago.edu/~grout/encyclopaedia_romana/wine/leadpoisoning.html

Thus, you do not need extensive calculations (There is some questions if the Roman could do such calculations, Roman roads were known to go in straight line ONLY, for that is easy to calculate. Any turns were 90 degrees even in hilly Italy. The Aqueducts structures we know of also tend to be straight lines EXCEPT when it comes to the parts on the ground (Which indicates the Romans used flow of water method for the ground based part of the Aqueducts, for flow of water could be adjusted for curves).

Thus my point, you do not need much calculations to make an Aqueduct. By its nature an Aqueduct is a simple device to carry water.