## 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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added addition adopted analysis appears applied Arabic arithmetic base basis beginning bers called cent CHAPTER characters circulate coins common common fraction compared comparison considered consists contained continued cube decimal definition denominator derived difference digits distinct divided division employed equal expressed factors figures five four fraction fundamental geometry give given greatest hence idea illustrate indicated interest Italy known length less letters means measure method multiplication nature nearly nine notation object obtained operations origin periods pound practice presented prime principle problem proportion quantity quotient ratio readily reasoning reduce regarded relation remainder repetend represent result root rule says scale seems seen similar simple square standard subtraction supposed symbol tens term things third tion true truths twelve units weight 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.