xvii ;;Quote: there is no empirical method without speculative concepts and no speculative thinking that does not stem from empirical material

5 ;;Quote: despite the edict against the opinion that the earth moves, Galileo sided with the Copernican view and showed that it was superior

6 ;;Quote: summary of Galileo's Dialog: experiments performed on the earth are independent of the earth's motion, celestial phenomena support the Copernican hypothesis, and the tides are due to the earth's movement

13 ;;Quote: three perpendiculars from an origin determine the three dimensions of length, breadth, and height with three unique, shortest lines

18 ;;Quote: whenever defects are seen in the foundations, it is reasonable to doubt everything else that is built upon them

18+;;Quote: need to establish new basic principles because Aristotle's views present many and grave difficulties

20 ;;Quote: a body at rest will move only under a natural tendency toward some particular place

20+;;Quote: for a body to acquire any degree of speed it must first pass through all gradations of lesser speed

24 ;;Quote: velocities are equal when the space passed is in the same proportion has as the time passed; more general than equal spaces in equal times

32 ;;Quote: Aristotle held that sensible experiments were better than human arguments

32+;;Quote: those who contradict the evidence of any sense deserved to lose that sense; e.g., heavy things go down and fire and air move up

41 ;;Quote: the celestial bodies are generable and corruptible like the earth; e.g., sun spots and the mountains on the moon as shown by the telescope

64 ;;Quote: the phases of the moon as seen from earth are the same as the phases of the earth as seen from the moon

103 ;;Quote: extensive knowledge is as nothing because understanding a thousand intelligibles is nothing to the infinity that exist

103+;;Quote: intensive knowledge, e.g., mathematics, equals the Divine in objective certainty because the knowledge is necessary

103 ;;Quote: our mathematical knowledge is the same as Divine wisdom but we reason by steps while His is one of simple intuition

103+;;Quote: mathematical knowledge is virtually included in the definition of all things

105 ;;Quote: writing is the greatest of all inventions because it allows one to communicate across vast distances and time

106 ;;Quote: two world views: the heavens are incorruptible and inalterable while the earth is corruptible and alterable, or the earth is a moving body like the moon and planets

108 ;;Quote: relying on the authority of Aristotle despite contradictory experience is like making an oracle out of a log of wood; e.g., nerves originating in the heart

116 ;;Quote: motion is relative to things at rest; among things that share equally in a motion, motion is as if it did not exist

116 ;;Quote: it is more sensible to rotate the earth than to rotate the skies; otherwise an immense number of extremely large bodies move with inconceivable velocities

116+;;Quote: nature does not act by means of many things when it can do so by means of a few

186 ;;Quote: from within a cabin below decks of a large ship, you can not distinguish standing still from moving uniformly

199 ;;Quote: Galileo used a diagram to represent the change in velocity of an object over equal times; probably the first such diagram

207 ;;Quote: a mathematical scientist must deduct material hindrances just as a merchant computer must discount the boxes from the weight of sugar

207+;;Quote: the results of mathematical science can agree with reality as accurately as do commercial calculations

207+;;Quote: a perfect, material sphere and a perfect, material plane would touch in just one point in the same way that a mathematical plane touches a mathematical sphere

217 ;;Quote: the tendency to throw off objects depends on the speed of revolution and not on the speed at the circumference; the earth moves too slowly to throw off stones

221 ;;Quote: the acceleration of straight motion in heavy bodies proceeds according to the odd numbers beginning from one; i.e., the spaces passed over are to each other as the squares of the times

229 ;;Quote: an accelerating object travels half the distance as an object in uniform motion at the final velocity; probably the first mathematical integration applied to mechanics

231 ;;Quote: the upper links of a pendulum's chain attempt to travel faster than the pendulum and thus lessen the pendulum's vibrations

235 ;;Quote: the upward motion of thrown objects is just as natural as the downward motion due to gravity

250 ;;Quote: if you throw an object down from the top of a tower, only the downward motion is sensible; the motion of the earth is independent

339 ;;Quote: Copernicus believed that Venus goes around the sun even though Venus when far from the earth was nearly the same size as it was when close to the earth

377 ;;Quote: the circumference of an infinite circle and a straight line are the same thing

425 ;;Quote: tides are caused by the motion of the earth jostling the seas, like a barge full of water