The Philosophy of Arithmetic as Developed from the Three Fundamental Processes of Synthesis, Analysis, and Comparison: Containing Also a History of Arithmetic |
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adopted Albert Girard algebra analysis apples Arabic system arithmetic arithmetical progression Avoirdupois bers called cent characters ciphers circulate coins common fraction comparison composite numbers consists contained continued fraction cube root cubic decimal fractions decimal scale definition Denominate Number denote derived difference digits divided dividend dominical letter elementary employed equal factors figures five four fractional units fundamental geometry given greatest common divisor hence idea illustrate integers Julius Cæsar large numbers least common multiple length letters mathematicians measure method metic minuend nature nine number expressed number is divisible obtained odd numbers operations origin periods pound presented prime number principle problem proportion quantity quotient ratio readily reasoning reckoned reduce regarded relation remainder repetend represent Roman rule seen sexagesimal simple square root standard Stevinus subtraction supposed symbol synthesis synthetic tens term tion Troy pound truths weight whole number write
Popular passages
Page 171 - All men are mortal, Socrates is a man, therefore Socrates is mortal, the subject and predicate of the major premiss are connotative terms, denoting objects and connoting attributes.
Page 298 - When a ray of light passes from one medium to another, it is refracted so that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities in the two media.
Page 298 - Therefore the specific gravity of a solid or a liquid body, is the ratio of its weight to the weight of an equal volume of water...
Page 269 - The square root of a number is one of the two equal factors of the number.
Page 173 - Lines drawn upon paper or upon the blackboard are not geometrical lines, since they have breadth and thickness. They represent geometrical lines. 25. A straight line is the shortest distance from one point to another point. 26. A curved line changes its direction at every point. 27. A broken line is not straight, but is made up of straight lines. 1. The line AB is a . 2. The line CD is a . 3. The line EF is a . 4.
Page 207 - Addition is the process of finding the sum of two or more numbers.
Page 274 - Therefore the cube of 25 equals the cube of the tens, plus three times the square of the tens into the units, plus three times the tens into the square of the units, plus the cube of the units.
Page 281 - Multiply the complete divisor by the trial figure, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 389 - If the two right-hand terms are ciphers, the number equals a number of hundreds, and since 100 is divisible by 4, any number of hundreds is divisible by 4. If the number expressed by the two right-hand digits is divisible by 4, the...
Page 273 - Multiply the divisor thus increased, by the last figure of the root ; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. 5th. Double the whole root already found, for a new divisor, and continue the operation as before, until all the periods are brought down. NOTE.