238 A SHORT HISTORY OF SCIENCE 



Geometry, Music, Astronomy, Cheiromancy, Cosmography, Necro- 

 mancy, Astrology, Perspective, and Prestidigitation ! A wonderfully 

 modest-looking gentleman, with his hand upon his heart, stands among 

 the number, with a you-do-me-too-much-honour look upon his coun- 

 tenance; Arithmetic and Geometry are pointing to him, and under 

 his feet his name is written Nicolo Tartalea. Morley, Jerome 

 Cardan. 



The Inventioni (1546) gives his solution of the cubic equation. 

 A treatise on Numbers and Measures (1556, 1560) gives a method 

 for finding the coefficients in the expansion of (1 + x) n for n = 2, 

 ... 6. It contains also a wide range of problems from commercial 

 arithmetic and a collection of mathematical puzzles. The follow- 

 ing examples may illustrate these : 



'Three beautiful ladies have for husbands three men, who are 

 young, handsome, and gallant, but also jealous. The party are 

 travelling, and find on the bank of a river, over which they have to 

 pass, a small boat which can hold no more than two persons. How 

 can they pass, it being agreed that, in order to avoid scandal, no 

 woman shall be left in the society of a man unless her husband is 

 present ? ' 



'A ship carrying as passengers 15 Turks and 15 Christians en- 

 counters a storm, and the pilot declares that in order to save the ship 

 and crew one half of the passengers must be thrown into the sea. 

 To choose the victims, the passengers are placed in a circle, and it is 

 agreed that every 9th man shall be cast overboard, reckoning from a 

 certain point. In what manner must they be arranged so that the 

 lot may fall exclusively upon the Turks?' 



' Three men robbed a gentleman of a vase containing 24 ounces of 

 balsam. Whilst running away they met in a wood with a glass-seller 

 of whom in a great hurry they purchased three vessels. On reaching a 

 place of safety they wish to divide the booty, but they find that their 

 vessels contain 5, 11, and 13 ounces respectively. How can they 

 divide the balsam into equal portions ? ' Ball. 



There is ho other treatise that gives as much information con- 

 cerning the arithmetic of the sixteenth century, either as to 

 theory or application. The life of the people, the customs of the 



