OF THE MENSURATION OF Running Waters.
Having, in the close of my Treatise of the Mensuration of Running Waters promised to declare upon another occasion other particulars more obscure, and of very great concern upon the same argumement: I now do perform my promise on the occasion that I had the past year 1641. to propound my thoughts touching the state of the Lake of Venice, a business certainly most important, as being the concernment of that most noble and most admirable City; and indeed of all Italy, yea of all Europe, Asia, & Africa; & one may truly say of all the whole World. And being to proceed according to the method necessary in Sciences, I will propose, in the first place certain Definitions of those Terms whereof we are to make use in our Discourse: and then, laying down certain Principles we will demonstrate some Problemes and Theoremes necessary for the understanding of those things which we are to deliver; and moreover, recounting sundry cases that have happened, we will prove by practice, of what utility this contemplation of the Measure of Running Waters is in the more important affairs both Publique and Private.
Two Rivers are said to move with equal velocity, when in equal times they passe spaces of equal length.
Rivers are said to move with like velocity, when their proportional parts do move alike, that is, the upper parts alike to the upper, and the lower to the lower; so that if the upper part of one River shall be more swift than the upper part of another; then also the lower part of the former shall be more swift than the part correspondent to it in the second, proportionally.