Prudens quaestio dimidium scientiae. - Roger Bacon

[H]aec vocatur scientia experimentalis, quae negligit argumenta, quoniam non certificant, quantumcunque sint fortia, nisi simul adsit experientia conclusionis. Et ideo haec docet experiri conclusiones nobiles omnium scientiarum, quae in aliis scientiis aut probantur per argumenta, aut investigantur per experientias naturales et imperfectas...

I use the example of the rainbow and of the phenomena connected with it, of which sort are the circle around the sun and the stars, likewise the rod lying at the side of the sun or of a star which appears to the eye in a straight line... called the rod by Seneca, and the circle is called the corona, which often has the colors of the rainbow. But neither Aristotle nor Avicenna, in their Natural Histories, has given us knowledge of things of this sort, nor has Seneca, who composed a special book on them. But Experimental Science makes certain of them. [The experimenter] considers rowers and he finds the same colors in the falling drops dripping from the raised oars when the solar rays penetrate drops of this sort. It is the same with waters falling from the wheels of a mill; and when a man sees the drops of dew in summer of a morning lying on the grass in the meadow or the field, he will see the colors. And in the same way when it rains, if he stands in a shady place and if the rays beyond it pass through dripping moisture, then the colors will appear in the shadow nearby; and very frequently of a night colors appear around the wax candle. Moreover, if a man in summer, when he rises from sleep and while his eyes are yet only partly opened, looks suddenly toward an aperture through which a ray of the sun enters, he will see colors. And if, while seated beyond the sun, he extend his hat before his eyes, he will see colors; and in the same way if he closes his eye, the same thing happens under the shade of the eyebrow; and again, the same phenomenon occurs through a glass vessel filled with water, placed in the rays of the sun. Or similarly if any one holding water in his mouth sprinkles it vigorously into the rays and stands to the side of the rays; and if rays in the proper position pass through an oil lamp hanging in the air, so that the light falls on the surface of the oil, colors will be produced. And so in an infinite number of ways, as well natural as artificial, colors of this sort appear, as the careful experimenter is able to discover.

Mathematics is the gate and key of the sciences. ... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy.