On the mathematical sciences and their offspring
Arithmetic and geometry as the two sciences; perspective the eye's art, nobler than music
A full page of mirror-script prose classifying the mathematical sciences, headed 'Of the mathematical sciences, and which are primitive and which derivative'. Leonardo names arithmetic and geometry as the two primitive sciences, covering discrete and continuous quantity, and derives perspective from geometry as its 'first daughter', concerned with the visual lines between object and eye. From perspective he in turn derives astronomy, which measures the celestial bodies with the visual line, and he ranks perspective, the science of the eye, far above music, which serves the lesser sense of hearing. The passage was recorded in the transcription.
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The two primitive mathematical sciences
Leonardo counts two mathematical sciences, arithmetic first and geometry second, extending over the two quantities, continuous and discrete, which embrace all things of the universe. Arithmetic, he adds, never needs geometry, whereas geometry in many cases avails itself of arithmetic.
Perspective, first daughter of geometry, above music
Perspective descends from geometry, its office extending over the visual lines between object and eye, from which astronomy is in turn born. Because it serves the eye, a nobler sense than the ear, Leonardo sets perspective far before music, and with it one figures the geometric bodies.