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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Common terms and phrases
adopted Albert Girard algebra analysis apples Arabic system arithmetic arithmetical progression Avoirdupois bers called cent characters ciphers circulate coins common fraction common multiple 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 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 Roman rule seen sexagesimal simple square root standard Stevinus subtraction supposed symbol synthesis tens term tion Troy pound truths twelve 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 181 - Multiplication is the process of taking one number as many times as there are units in another number.
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 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.
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 257 - The Least Common Multiple of two or more numbers is the least number which is a multiple of each of them; thus, 12 is the least common multiple of 2, 3, and 4.
Page 173 - Things that are equal to the same thing are equal to each other; " and if they are severally unequal, we have a case of mean proportionals. In the second form, if A, B, and C...
Page 269 - The square root of a number is one of the two equal factors of the number.
Page 207 - Addition is the process of finding the sum of two or more numbers.
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...