On Geometry (1600-1649)

"Where there is matter, there is geometry." (Johannes Kepler, "Concerning the More Certain Fundamentals of Astrology", 1601)

"Geometry is one and eternal shining in the mind of God. That share in it accorded to men is one of the reasons that Man is the image of God." (Johannes Kepler, "Conversation with the Sidereal Messenger" ["Dissertatio cum Nuncio Sidereo"], [open letter to Galileo Galilei] 1610)

"Thus the analysis of angular sections involves geometric and arithmetic secrets which hitherto have been penetrated by no one." (François Viète, cca 1615)

"Mathematic is either Pure or Mixed: To Pure Mathematic belong those sciences which handle Quantity entirely severed from matter and from axioms of natural philosophy. These are two, Geometry and Arithmetic; the one handling quantity continued, the other dissevered. [...] Mixed Mathematic has for its subject some axioms and parts of natural philosophy, and considers quantity in so far as it assists to explain, demonstrate and actuate these." (Francis Bacon, "De Augmentis", 1623)

"Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth." (Galileo Galilei, "The Assayer", 1623)

"And having thus passed the principles of arithmetic, geometry, astronomy, and geography, with a general compact of physics, they may descend in mathematics to the instrumental science of trigonometry, and from thence to fortification, architecture, engineering, or navigation. And in natural philosophy they may proceed leisurely from the history of meteors, minerals, plants, and living creatures, as far as anatomy. Then also in course might be read to them out of some not tedious writer the institution of physic. […] To set forward all these proceedings in nature and mathematics, what hinders but that they may procure, as oft as shall be needful, the helpful experiences of hunters, fowlers, fishermen, shepherds, gardeners, apothecaries; and in other sciences, architects, engineers, mariners, anatomists." (John Milton, "On Education", 1644)

"In geometry, to be sure, the accident of a fraction or an irrational does not usually prevent equations from being solved readily. nor does the imperfection of a negative, for the subject on which the geometer works is always certain. But multiplicity of affections8 is a hindrance, and the higher the power and the order of an affection, the more likely it is that a fraction or surd9 will appear in the solution of a problem." (François Viète, "On the Structure of Equations as Shown by Zetetics, Plasmatic Modification and Syncrisis", 1646)