Jules Hoüel Signed Autograph Letter To Charles-ange Laisant Mathematics

Autograph letter signed to charles-angels leaving. Signed autograph letter, bordeaux, December 26, 1883, 4 pages, to charles-angels laizing. Exceptional letter on how to draw a sinus table by means of the abbreviated multiplication. Jules hoüel devoted much of his work on the foundations of infinitesimal calculus and the construction of digital tables. Its method thus allows to determine the logarithm of a number or the number corresponding to a logarithm with five exact decimal places.

In this letter he develops his method of abbreviated multiplication entirely and explains his "great discovery". It then continues on the construction of a 3 decimal logarithm table. In his scholarly presentation, he also mentions the work of mathematicians william oughtred, thomas simpson, urban the glassmaker and giusto bellavitis. I don't want to let the year end without giving you a sign of life. I become so inert, by the effect of premature old age, that I have lost all ability to act, all memory. I do not forget my friends; but I never find time to write to them, always prevented by other occupations, all of them most urgent than others. I take advantage of the little lucidity I have left to answer the subject of your last letter. I do not know if I can in all its simplicity the way that I had found to draw up a sinus table very quickly by means only of the abbreviated multiplication. First of all, here is how I have the calculation of the abbreviated multiplication. Now you want to build a 3 decimal logarithm table. First for sinus and cosinus, 10 degrees in 10 degrees. Let's first look for the sinuse. 9° correspond to an axis of length p/2 = 1.5708.

The length of the 10° axis is therefore, keeping the 4th decimal place, 0,1745 instead of 1736. The cosinus is calculated by the formula cos x = v1-sin2x. Calculation of sin2x 0.1745 0.1745 _______ 0.01745 1221 70 _______ sin2x = 0.0305 _______ cos2x = 0.9695. Extraction of the abbreviated square root.

Cos x = 0.9846, instead of the exact value 0.9848. You see that the calculations are all the easier because the intervals are closer. When, for example, the values of the sinus and cosinus are 1°, the table can be completed very quickly by the known formulae of thomas simpson. There isn't one for a quarter of an hour of work, and it's an excellent numerical computing exercise. I don't know if you can read my galimatia. If it's too confusing, I'll try to start over with more clarity. Once you have this small table, to which you can, by easy-to-find formulas, add a table of tangents, you can, by means of the calculation rule. Of which the glassmaker knew how to disgust the French, and this is not what he did best, - solve in the race all possible triangles. English and Russian translations available on request.

Third Republic at peace (france). Guillaume-jules hoüel is a French mathematician. Charles-ange leaving is a French military, mathematician and politician. More information about jules hoüel. More information on laminating charms-angels.

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subtype: autograph on paper
theme: mathematics
type: autograph, dedication
number of pages: 4