By Galileo Galilei
This vintage encompasses 30 years of hugely unique experiments and theories. Its energetic expositions speak about dynamics, elasticity, sound, power of fabrics, and extra. Orginally translated in 1914, this vintage team and Salvio English translation is now on hand in a unique digital model.
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Extra resources for Dialogues Concerning Two New Sciences
This being granted we must say that there are as many squares as there are numbers because they are just as numerous as their roots, and all the numbers are roots. Yet a t the outset we said there are many more numbers than squares, since the larger portion of them are not squares. Not only so, but the proportionate number of squares diminishes as we pass to larger numbers. Thus up to 1 0 0 we have IO squares, that is, the squares constitute 1 / 1 0 part of all the numbers; up to 1oo00, we find only I / I [791 part to be squares; and up to a million only I/IOOOpart; on the other hand in an infinite number, if one could conceive of such a thing, he would be forced to admit that there are as many squares as there are numbers all taken together.
And 4; then 3 is the mean proportional between 9 and I ;while 2 is a mean proportional between 4 and I ;between 9 and 4 we have 6 as a mean proportional. A property of cubes is that they must have between them two mean proportional numbers; take 8 and 27; between them lie 12 and 18; while between - ----- ------ - - SECOND DAY R. While Simplicio and I were awaiting your arrival we were trying to recall that last consideration which you advanced as a principle and basis for the results you intended to obtain; this consideration dealt with the resistance which all solids offer to fra&ure and depended upon a certain cement which held the parts glued together so that they would yield and separate only under considerable pull botente uttruzzione].
And thus we have a continuous quantity built up of an infinite number of indivisibles. But if we can carry on indefinitely the division into finite parts what necessity is there then for the introduction of non-finite parts? The very fa& that one is able to continue, without end, the division into finite parts [inparti quante] makes it necessary to regard the quantity as composed of an infinite number of immeasurably small elements [di infiniti non quantzl. Now in order to settle this matter I shall ask you to tell me whether, in your opinion, a continuum is made up of a finite or of an infinite number of finite parts [parti quante].
Dialogues Concerning Two New Sciences by Galileo Galilei