But to me all sciences seem vain and full of error that are not born of experience, mother of all certainty, and do not terminate in an actual experience.
Poor is the pupil who does not surpass his master.
There is no result in nature without a cause; understand the cause and you will have no need of the experiment.
Therefore, O students, study mathematics and do not build without foundations.
For once you have tasted flight you will walk the earth with your eyes turned skywards, for there you have been and there you will long to return.
The eye, the window of the soul, is the chief means whereby the understanding can most fully and abundantly appreciate the infinite works of Nature; and the ear is second.
Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.
Truth was the only daughter of Time.
The body of the earth is of the nature of a fish... because it draws water as its breath instead of air.
A bird maintains itself in the air by imperceptible balancing, when near to the mountains or lofty ocean crags; it does this by means of the curves of the winds which as they strike against these projections, being forced to preserve their first impetus bend their straight course towards the sky with divers revolutions, at the beginning of which the birds come to a stop with their wings open, receiving underneath themselves the continual buffetings of the reflex courses of the winds.
A bird is an instrument working according to mathematical law, which instrument it is within the capacity of man to reproduce with all its movements, but not with a corresponding degree of strength, though it is deficient only in the power of maintaining equilibrium. We may therefore say that such an instrument constructed by man is lacking in nothing except the life of the bird, and this life must needs be supplied from that of man.
Why are the bones of great fishes, and oysters and corals and various other shells and sea-snails, found on the high tops of mountains that border the sea, in the same way in which they are found in the depths of the sea?
Although human ingenuity may devise various inventions which, by the help of various instruments, answer to one and the same purpose, yet will it never discover any inventions more beautiful, more simple or more practical than those of nature, because in her inventions there is nothing lacking and nothing superfluous; and she makes use of no counterpoise when she constructs the limbs of animals in such a way as to correspond to the motion of their bodies, but she puts into them the soul of the body.
Let proportion be found not only in numbers and measures, but also in sounds, weights, times, and positions, and what ever force there is.
Necessity is the mistress and guide of nature. Necessity is the theme and inventress of nature, her curb and her eternal law.
Perspective is a most subtle discovery in mathematical studies, for by means of lines it causes to appear distant that which is near, and large that which is small.
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