"I had scarcely entered the room when I saw on my table an open book I had not put there. It was the works of Cardano. I did not intend to read it, but my gaze fell as though compelled on a story told by that philosopher. He writes that he was studying one night by candlelight when he saw two tall old men come in through the closed doors of his room. He asked them many questions, and they finally told him they were from the Moon; whereupon they disappeared. I was so surprised, both by the book that had put itself on my table and by the page it was open to, that I took this chain of events for an inspiration from God, who was urging me to tell people that the Moon is a world." (Cyrano de Bergerac, "The Other World", 1657)
"But if now a simple, that is, a linear equation, is multiplied by a quadratic, a cubic equation will result, which will have real roots if the quadratic is possible, or two imaginary roots and only one real one if the quadratic is impossible. […] How can it be, that a real quantity, a root of the proposed equation, is expressed by the intervention of an imaginary? For this is the remarkable thing, that, as calculation shows, such an imaginary quantity is only observed to enter those cubic equations that have no imaginary root, all their roots being real or possible, as has been shown by trisection of an angle, by Albert Girard and others. […] This difficulty has been too much for all writers on algebra up to the present, and they have all said they that in this case Cardano’s rules fail." (Gottfried W Leibniz, cca. 1675)
" It appears [...] from this short chapter [Ars Magna, lib x. ch. 1], that he had discovered most of the principal properties of the roots of equations, and could point out the number and nature of the roots, partly from the signs of the terms, and partly from the magnitude and relations of the co-efficients." (Charles Hutton, "Algebra" [in "A Mathematical and Philosophical Dictionary", 1795)
"The Ars Magna is a great advance on any algebra previously published. Hitherto algebraists had confined their attention to those roots of equations which were positive. Cardan discussed negative and even complex roots, and proved that the latter would always occur in pairs, though he declined to commit himself to any explanation as to the meaning of these 'sophistic' quantities which he said were ingenious though useless." (W W Rouse Ball, "A Short Account of the History of Mathematics", 1888)
"The application of the theory [of probability] to mortality tables in any large way may be said to have started with John Graunt [...] The first tables of great importance, however, were those of Edmund Halley [...] however [...] Cardan seems to have been the first to have been the first to consider the problem in a printed work, although his treatment is very fanciful. He gives a brief table in his proposition 'Spatium vitae naturalis per spatium vitae fortuitum declarare', this appearing in the De Proportionibus Libri V [...]" (David E Smith (Ed.), "History of Mathematics" Vol. 2, 1925)
"The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). This was devoted primarily to the solution of algebraic equations. It contained the solution of the cubic and biquadratic equations, made use of complex numbers, and in general may be said to have been the first step toward modern algebra." (David E Smith (Ed.), "History of Mathematics" Vol. 2, 1925)
"Most important for the history of science is the fact that Liber de Ludo Aleae,'The Book of Games of Chance', contains the first study of the principles of probability. [...] it would seem much more just to date the beginnings of probability theory from Cardano's treatise rather than the customary reckoning from Pascal's discussions with his friend de Méré and the ensuing correspondence with Fermat [...] at least a century after Cardano [...]" (Oystein Ore [Ed.], "Cardano the Gambling Scholar", 1953)
"Cardano reasoned that the end of man is to know God and to mediate between the divine and the mortal. The rational soul is immortal and when permeated with light is inseparable from God. True wisdom is gained from union with God and by mathematics, as God has subjected the world to mathematical law." (Albert E Avey, "Handbook in the History of Philosophy", 1954)
"Insolving the cubic and quartic equations, Cardan and Ferrari implicitly assumed the existence of roots [...]. Girard, in the early seventeenth century, was one of the first to assert the existence of roots, real or imaginary, though 'imaginary root' did not have a clear meaning in his work. As people became more comfortable with complex numbers, the existence of roots evolved into the existence of complex roots, which come in complex conjugate pairs when the coefficients are real. Thus the eighteenth-century version of the Fundamental Theorem of Algebra asserts that every nonconstant polynomial in R[x] factors into linear and quadratic factors with coefficients in R." (David A Cox, "Galois Theory" 2nd Ed., 2012)
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