Mathematics, such as appertain to painting, are necessary to the painter, also the absence of companions who are alien to his studies: his brain must be versatile and susceptible to the variety of objects which it encounters, and free from distracting cares.
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As every divided kingdom falls, so every mind divided between many studies confounds and saps itself.
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The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.
No human investigation can be called real science if it cannot be demonstrated mathematically.
Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics.
Those who condemn the supreme certainty of mathematics feed on confusion, and can never silence the contradictions of the sophistical sciences which lead to eternal quackery.
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