In 1647, Gregoire de Saint-Vincent published his book, Opus geometricum quadraturae circuli et sectionum coni (Geometric work of squaring the circle and conic sections), vol. 2 (Antwerp, (Belgium): Johannes and Jakob Meursius, 1647). On page 586, Proposition CIX, he proves that if the abscissas of points are in geometric proportion, then the areas between a hyperbola and the abscissas are in arithmetic proportion. This finding allowed Saint-Vincent's former student, Alphonse Antonio de Sarasa, to prove that the area between a hyperbola and the abscissa of a point is proportional to the abscissa's logarithm, thus uniting the algebra of logarithms with the geometry of hyperbolas. See: Alphonse Antonio de Sarasa, Solutio problematis a R.P. Marino Mersenne Minimo propositi ... [Solution to a problem proposed by the reverend father Marin Mersenne, member of the Minim order ... ], (Antwerp, (Belgium): Johannes and Jakob Meursius, 1649). Sarasa's critical finding occurs on page 16 (near the bottom of the page), where he states: "Unde hae superficies supplere possunt locum logarithmorum datorum ... " (Whence these areas can fill the place of the given logarithms ... ). [In other words, the areas are proportional to the logarithms.] See also: Enrique A. González-Velasco, Journey through Mathematics: Creative Episodes in Its History (New York, New York: Springer, 2011), page 118.
In 1647, Gregoire de Saint-Vincent published his book, Opus geometricum quadraturae circuli et sectionum coni (Geometric work of squaring the circle and conic sections), vol. 2 (Antwerp, (Belgium): Johannes and Jakob Meursius, 1647). On page 586, Proposition CIX, he proves that if the abscissas of points are in geometric proportion, then the areas between a hyperbola and the abscissas are in arithmetic proportion. This finding allowed Saint-Vincent's former student, Alphonse Antonio de Sarasa, to prove that the area between a hyperbola and the abscissa of a point is proportional to the abscissa's logarithm, thus uniting the algebra of logarithms with the geometry of hyperbolas. See: Alphonse Antonio de Sarasa, Solutio problematis a R.P. Marino Mersenne Minimo propositi ... [Solution to a problem proposed by the reverend father Marin Mersenne, member of the Minim order ... ], (Antwerp, (Belgium): Johannes and Jakob Meursius, 1649). Sarasa's critical finding occurs on page 16 (near the bottom of the page), where he states: "Unde hae superficies supplere possunt locum logarithmorum datorum ... " (Whence these areas can fill the place of the given logarithms ... ). [In other words, the areas are proportional to the logarithms.] See also: Enrique A. González-Velasco, Journey through Mathematics: Creative Episodes in Its History (New York, New York: Springer, 2011), page 118.
Jost Bürgi, Arithmetische und Geometrische Progress Tabulen … [Arithmetic and Geometric Progression Tables … ], (Prague, (Czech Republic): University [of Prague] Press, 1620). Available on-line at: Bavarian State Library, Germany Unfortunately, Bürgi did not include, with his table, instructions for using the table. Neither the table nor the instructions were published, apparently only proof sheets of the table were printed. The contents of the instructions were reproduced in: Hermann Robert Gieswald, Justus Byrg als Mathematiker, und dessen Einleitung zu seinen Logarithmen [Justus Byrg as a mathematician, and an introduction to his logarithms] (Danzig, Prussia: St. Johannisschule, 1856), pages 26 ff.
Jost Bürgi, Arithmetische und Geometrische Progress Tabulen … [Arithmetic and Geometric Progression Tables … ], (Prague, (Czech Republic): University [of Prague] Press, 1620). Available on-line at: Bavarian State Library, Germany Unfortunately, Bürgi did not include, with his table, instructions for using the table. Neither the table nor the instructions were published, apparently only proof sheets of the table were printed. The contents of the instructions were reproduced in: Hermann Robert Gieswald, Justus Byrg als Mathematiker, und dessen Einleitung zu seinen Logarithmen [Justus Byrg as a mathematician, and an introduction to his logarithms] (Danzig, Prussia: St. Johannisschule, 1856), pages 26 ff.
doi.org
Bruce, I. (2002). "The Agony and the Ecstasy: The Development of Logarithms by Henry Briggs". The Mathematical Gazette. 86 (506): 216–227. doi:10.2307/3621843. JSTOR3621843. S2CID125835646.
Bruce, I. (2002). "The Agony and the Ecstasy: The Development of Logarithms by Henry Briggs". The Mathematical Gazette. 86 (506): 216–227. doi:10.2307/3621843. JSTOR3621843. S2CID125835646.
Bruce, I. (2002). "The Agony and the Ecstasy: The Development of Logarithms by Henry Briggs". The Mathematical Gazette. 86 (506): 216–227. doi:10.2307/3621843. JSTOR3621843. S2CID125835646.
