Algebra
CLAVIUS, CHRISTOPHORUS

Rome Batholommeo Zannetti 1608 4to. (22.3 x 16.3 cm). Contemporary vellum; wear to edges and some loss to ends of spines, turn-ins partly sprung. Collation: [36], 383,[1] pp. lacking front free end paper. Foxing on edges near end of book. Clavius was a Jesuit who contributed to astronomy and mathematics. Very Good Contemporary vellum (Item ID: 0000546)

$3,500.00

"Christopher Clavius published the first edition of his algebra textbook in 1608, in Rome, by Zannetti. [Clavius C., Algebra, Geneva, 1609.] Leibnitz wrote a letter to Bernoulli in 1703, indicating that he learned algebra from Clavius' book. As a child, I had studied the elementary algebra of one Lancius, and later that of Clavius. The task of algebra, solving equations, had to realize four stages: firstly, putting the verbally formulated, word problem, into an equation; next to reduce the equation, that is to put homogeneous terms on the same side; thirdly to divide the highest power of the equation by its coefficient to have the unknown not affected by coefficients other than 1; and lastly, if necessary, to extract the respective root in order to get the value for the unknown. This is surprisingly unsophisticated. Basically, it corresponds to what Al-Khwarizmi had already given as the rule: al-jabr and al-muqabala are just these reduction procedures. Clavius, hence, does not present a theoretical program for algebra: it is rather a set of practical rules. In fact, there do not follow systematizations of types of equations and standard procedures for their solution. The book continues to present and discuss examples of problems. In fact, the bulk of the remainder of the volume, with its 383 pages, consists of four chapters with an immense number of problems and their solutions. Characteristically, the titles of these three chapters begin by Aenigmata, i.e. riddles. This recalls the style and contents of Arab treatises and Italian treatises, from Fibonacci on, in particular of the trattati d'abbaco. Problems used to be given there in a recreational manner. Clavius calculated and published a table of sines and cosines with 7 decimal places in his book Astrolabium. For each value of degrees and minutes, the table gives the value of the sine and cosine with the precision of one part in ten million. Unlike other tables then in circulation, he was very careful to avoid errors. He showed how to interpolate to get precise values for fractions of seconds of arc. This significantly shortened computations in astronomy and spherical geometry. Clavius was the first to use a decimal point, some twenty years before it became common; the first to use parentheses to collect terms; and the first to use the plus and minus signs + and - in Italy. Likewise, he used no sign for equality and expressed it verbally, too. For instance, for establishing an equation, he put: aequatio sit inter 5x + 7 & 1x." (Sigismondi C., IL NUOVO CIMENTO ,2012)

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