## Dialogues Concerning Two New Sciences |

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able accelerated acquired altitude angle ball base bears body break carry circle clear consider cubits cylinder demonstrated descent described diameter diminishes discussion distance draw drawn elevation entire equal experiment fact fall figure finite follows force four given greater half heavy Hence horizontal inclined plane increase infinite interval larger length less manner matter mean proportional measure medium momentum motion moving namely nature observed parabola parallel pass perpendicular polygon portion prism problem produced PROPOSITION prove ratio reach rectangle remain represent resistance rest result SAGR Salv side similar SIMP Simplicio smaller solid space speed square starting string surface THEOREM time-interval tion traversed triangle true twice understand uniform vacuum vertical vibrations volume weight

### Popular passages

Page 153 - It has been observed that missiles and projectiles describe a curved path of some sort; however no one has pointed out the fact that this path is a parabola. But this and other facts, not few in number or less worth knowing, I have succeeded in proving...

Page 154 - ... path of some sort; however, no one has pointed out the fact that this path is a parabola. But this and other facts, not few in number or less worth knowing, I have succeeded in proving; and what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners.

Page 215 - Furthermore, we may remark that any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of acceleration or retardation are removed, a condition which is found only on horizontal planes; for in the case of planes which slope downwards there is already present a cause of acceleration, while on planes sloping upward there is retardation; from this it follows that motion along a horizontal plane is perpetual; for, if the velocity be uniform, it cannot be...

Page 160 - ... but we have decided to consider the phenomena of bodies falling with an acceleration such as actually occurs in nature and to make this definition of accelerated motion exhibit the essential features of observed accelerated motions.

Page 65 - an iron ball of one hundred pounds falling from a height of one hundred cubits reaches the ground before a one-pound ball has fallen a single cubit.

Page 172 - SALv. I do not wish, Sagredo, that we trouble ourselves too much about this matter, since we are going to apply this principle mainly in motions which occur on plane surfaces, and not upon curved, along which acceleration varies in a manner greatly different from that which we have assumed for planes.

Page 131 - Clearly then if one wishes to maintain in a great giant the same proportion of limb as that found in an ordinary man he must either find a harder and stronger material for making the bones, or he must admit a diminution of strength...

Page 176 - ... lines [which represent time], differences which exceed one another by equal amounts, this excess being equal to the smallest line [viz. the one representing a single time-interval]: or we may say [that this is the ratio] of the differences of the squares of the natural numbers beginning with unity.

Page 62 - But, even without further experiment, it is possible to prove clearly, by means of a short and conclusive argument, that a heavier body does not move more rapidly than a lighter one provided both bodies are of the same material and in short such as those mentioned by Aristotle.

Page 161 - ... we may picture to our mind a motion as uniformly and continuously accelerated when, during any equal intervals of time whatever, equal increments of speed are given to it.