The Philosophy of Arithmetic: Exhibiting a Progressive View of the Theory and Practice of Calculation, with Tables for the Multiplication of Numbers as Far as One Thousand
W. and C. Tait, 1820 - Arithmetic - 258 pages
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The Philosophy of Arithmetic: Exhibiting a Progressive View of the Theory ...
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added addition adopted amount annexed appear Arithmetic beginning Binary calculation called carried changed characters circle collected combined complete consequently consisting contained continued converted corresponding coun decimal Denary Scale denominator denoted descending digits divided division divisor double eight eleven employed equal Europe evidently example excess exhibited expressed figures five four fourth bar fraction full counters gives Greeks hand hence higher hundred joined leave letters likewise lines lower marks mode multiplicand multiplied nearly nine notation Note once open counters operation original pair performed period Persians practice present principle progress Quaternary Scale quotient reckoned reduced remainder repeated represented result Romans root rows second bar seven signify similar single square step strokes subtraction successive Suppose taken tens terminates ters third bar thousand tion twice units whole
Page 239 - Alter erit tum Tiphys, et altera quae vehat Argo Delectos heroas ; erunt etiam altera bella, Atque iterum ad Trojam magnus mittetur Achilles.
Page 99 - The teller sat about the middle of the table 5 on his right hand, eleven pennies were heaped on the first bar, and a pile of nineteen shillings on the second ; while a quantity of pounds was collected opposite to him, on the third bar. For the sake of expedition, he might employ a different mark, to represent half the value of any bar, a silver penny for ten shillings, and a gold penny for ten pounds.
Page 99 - ... nineteen shillings on the second, while a quantity of pounds was collected opposite to him, on the third bar. For the sake of expedition he might employ a different mark to represent half the value of any bar, a silver penny for ten shillings, and a gold penny for ten pounds. In early times, a checkered board, the emblem of calculation, was hung out, to indicate an office for changing money. It was afterwards adopted as the sign of an inn or hostelry, where victuals were sold, or strangers lodged...
Page 95 - ... to denote units, tens, hundreds, thousands, &c. The labour of counting and arranging those pebbles was afterwards sensibly abridged, by drawing across the board a horizontal line, above which, each single pebble had the power of five. In the progress of luxury, tali, or dies made of ivory, were used instead of pebbles, and small silver coins came to supply the place of counters. But the operations with...
Page 244 - Prove that the product of the sum and difference of any two numbers is equal to the square of the first, minus the square of the second.
Page 219 - It consists of a small oblong board surrounded by a high ledge, and parted lengthwise near the top by another ledge. It is...
Page 201 - RULE. — Multiply all the numerators together for a new numerator, and all the denominators for a new denominator ; then reduce the new fraction to its lowest terms.
Page 102 - French verb lailler, to cut, because they are squared at each end. The sum of money was marked on the side with notches, by the cutter of tallies, and likewise inscribed on both sides in Roman characters, by the writer of the tallies. The smallest notch signified a penny, a larger one a shilling, and one still larger a pound; but other notches, increasing successively in breadth, were made to denote ten, a hundred, and a thousand. The stick was then cleft through the middle by the...
Page 176 - Vertical lines being drawn and the numbers distinguished into periods of two figures, the nearest root of 10 is 3, which is placed both below and above, and its square, 9, subtracted ; the 3 is now doubled, and 6 being written in the next column, is contained twice in 17, or the remainder with the first figure of the next period; the 2 is therefore set down both above and below, and being multiplied into 6 gives 12, which is subtracted from 17, leaving 5 ; the square of 2, or 4, is now subtracted...
Page 219 - Ful fetisly ydight with herbes sote, And he himself was swete as is the rote Of licoris, or any setewale. His almageste, and bokes gret and smale, His astrelabre, longing for his art, His augrim stones, layen faire apart On shelves couched at his beddes hed, His presse ycovered with a falding red.