## Quotes from Leonardo da Vinci's notebooks

Below we give a number of quotes from Leonardo da Vinci's notebooks which seem relevant to mathematics and the mathematical sciences.

- It seems to me that all sciences are vain and full of errors unless they are born of experience, the mother of all certainty ... that is to say, those that no not at their beginning, middle or end, pass through any of the five senses ... where there is not reason its place is taken by chaos. This never happens when things are certain. Therefore, where there are disputes there is no true science ... wherever it is known, controversy is silenced for all time.

- The eye counsels and corrects all the arts of mankind ... it is the prince of mathematics, and those sciences which are founded on it are absolutely certain. It has measured the distances and sizes of the stars, it has discovered the elements and their locations ... it has given birth to architecture and to perspective and to the divine art of painting.

- Linear perspective deals with the action of the lines of sight, in proving by measurement how much smaller the second object is than the first, and how much the third is smaller than the second, and so on by degrees to the limit of things visible.

- I find by experience that if a second object is as far beyond the first as the first is from the eye, although they are the same size, the second will seem half the size of the first, and if the third object is the same size as the second and the third is as far beyond the second as the second is from the first, it will appear to be half the size of the second, and so on by degrees, at equal distances.

- Good judgement proceeds from a clear understanding, and a clear understanding comes from reason derived from sound rules, and sound rules are the daughters of sound experience - the common mother of all the sciences and arts.

- There is no certainty where one can neither apply any of the mathematical sciences nor any of those which are connected with the mathematical sciences.

- Those who condemn the supreme certainty of mathematics encourage confusion, and can never stop the contradictions of the sophistical sciences which lead to eternal falsehoods.

- Mechanics is the paradise of mathematical science because by its means one arrives at the fruits of mathematics.

- If you throw a stone into a pond the waves which hit the sides are thrown back towards the place where the stone hit the water; and on meeting other waves they never intercept each other's course. ... In a small pond the one hit gives rise to many motions which advance and recoil.

- Just as the stone thrown into water become the centre and cause of various circles, so the sound made in the air spreads out in circles and fills the surrounding parts with an infinite image of itself.

- Nature does not break her laws but is constrained by the logical necessity of the law which is inherent in her.