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PREFACE.

practice. Literal calculation original: "Le calcul litteral"; the use of letters to represent variables (algebra), rather than specific numbers, which allows for universal solutions. has this advantage: it spares the capacity of the mind by presenting an infinite number of objects under the simplest expression, without being distracted by the complexity of their relationships. It is enough to pay attention only to the rules of calculation, and the pen alone leads directly to the resolution one seeks. This then becomes a general formula for all similar questions, without needing any demonstrations other than those drawn from the clarity of the calculation itself, whose operations are founded on simple axioms Self-evident truths that require no proof, such as "the whole is greater than the part.". Often a single algebraic expression sheds light on an entire Science, from which one easily develops all the consequences one after another, as can be judged by the way we have expressed the rules of motion and those for the measurement of water original: "mesure des Eaux"; referring to hydraulics and the flow rates of rivers and pipes.. However, as my intention has been to ensure this Work becomes useful to all those who read it, I have taken care to set out in the form of maxims all the rules I have deduced from ordinary Analysis Standard algebra. and the new Calculations original: "nouveaux Calculs"; this refers to the infinitesimal calculus (differential and integral) which was a cutting-edge mathematical tool in the early 18th century.. I have even applied these Maxims to numerical examples, so that readers might become more familiar with them and use them with the same confidence that most people usually have for the operations of Practical Geometry, even though they may be ignorant of the theory that provided them.

I was on the eve of publishing the Treatise I had promised in 1729 on Hydraulic Architecture, which was to encompass (as I announced then) only the different works of Masonry, Carpentry, and Fascine work original: "Fascinage"; the use of bundles of sticks or brushwood to stabilize soil, create riverbanks, or build foundations in water. that are performed in water. However, when I set out to design a Machine to raise water, I was very surprised to find I did not know how to go about accurately determining all its parts in such a way as to satisfy a discerning mind that might have asked me to account for the arrangement of each...