GENERAL PREFACE

quadrant. Many other things may be seen in the books of Archimedes and in the supplement to them, which the Synopsis original: "Synopsis". This refers to Mersenne's own "Synopsis mathematica" published in 1626, which collected various mathematical works. displays.

XVII. Concerning water jets, both vertical and middle, it should be observed that various rainbows are represented when the eye is placed between them and the sun. This also happens from water sprayed from the mouth, and from a jet; likewise from bubbles made of soap; from flasks and glass jars full of water; from a crystalline prism; and from wet, moist eyes looking at the light of a candle or the sun.

XVIII. It should also be noted regarding proposition 53 of the Hydraulics that the digging of wells is often subject to great dangers. This is not only because of the foul odors exhaling from certain parts of the earth, but also from the air. Even if it is not infected, it may be opposed to breathing from every side. This air extinguishes light and fire, and it kills men as they descend. This happens unless you pull them back immediately at a signal given by the tug of a rope. You should move the face and head of the half-dead man to a newly made little hole where the green turf has been removed. By this method, those among the English return from their faint. These people dig a second well twenty feet away. They connect both wells by a hole in the earth placed between them. Fire is then applied to pull the aforementioned suffocating air out. After this, someone may descend into that well without danger to dig out the coals for the hearth, from which great revenues come. This is also commonly done at Liège and in many other places.

That fire is lit at the mouth of the hole connecting both wells. It thins the air near it and draws the suffocating air from the first well. This happens in almost the same way as a fire lit in our hearths and rooms. It draws in the outside air through the cracks of the windows and doors and other small holes to replace the air in the room, which goes out through the chimney with the flame. This is proven by various whistling sounds and winds. From this, the Urinatores: Specialized salvage divers who practiced breath-holding techniques. could devise a way of breathing under the water, which will be discussed in the book on Navigation.

Furthermore, where the wells of the Amsterdammers were discussed on pages 219 and 220, add that the workers and those in charge of the digging sink wooden pipes into the hole. They go all the way to the bottom where the drinkable water is found. They are joined with such skill that the outer sea water cannot enter them. Thus, the joined pipes form a single channel, as it were. From this, you may later draw water whenever you wish with a piston or plunger, as was said in proposition 38 of the Hydraulics.

XIX. To those things which were said about numbers at the end of proposition 20 on Projectiles and point 14 of the Preface to the Hydraulics, add the discovered art by which numbers may be found, as many as you wish. These numbers, when their aliquot parts Aliquot parts are the proper divisors of a number, such as 1, 2, and 3 for the number 6. are reduced into a single sum, have not only a double ratio (such as 120, the smallest of all; 672; 523,776; 1,476,304,896; and