FOREWORD.

...works and currents, for which the various effects are calculated in the most advantageous cases, while demonstrating the defects and advantages of these machines and what would be required to make them perfect.

The fifth chapter begins with a discourse on the great works that the Romans constructed for the transport of water, followed by a description of the machine applied to the Notre-Dame bridge in Paris The Pont Notre-Dame waterwheel was a landmark of 18th-century engineering, providing water to the city of Paris., accompanied by developments of new pumps to rectify it, and the calculations that determine its output.

Regarding the fourth Book, it is also divided into five Chapters: the first begins with the description and calculation of the effect of a machine that I have imagined, which has nothing in common with any of those put into use until now. Its purpose is to make water from a fall raise itself to whatever height one desires, without any constraint; following this, we report several others executed for the same purpose in Paris and in England.

In the second chapter, we examine the action of water in conduit pipes Pipes used to transport water from a source to a reservoir or fountain. and the friction that retards its speed, from which we deduce all the rules necessary to know on this subject, accompanied by a great number of experiments and useful remarks.

The third begins with a historical discourse on the origin and progress of machines moved by the action of fire These "fire-driven machines" are early steam engines, specifically the Newcomen atmospheric engine, which Bélidor was among the first to analyze mathematically.; we provide one as an example, detailed down to its smallest parts. We calculate its effect relative to the force of the steam of boiling water, the resistance of the atmosphere, and the weight of the water column one wishes to raise; then, we report a great number of other machines moved by animals and currents for drawing water from very deep mines and wells.