6.When the tables are computed, the fractions following the period may then be rejected without any sensible error. For in our large numbers, an error which does not exceed unity is insensible and as if it were none.
Thus in the completed table, instead of 9987643.8213051, which is , we may put 9987643 without sensible error.
7.Besides this, there ts another rule for accuracy; that is to say, when an unknown or incommensurable quantity is included between numerical limits not differing by many units.
Thus if the diameter of a circle contain 497 parts, since it is not possible to ascertain precisely of how many parts the circumference consists, the more experienced, in accordance with the views of Archimedes, have enclosed it within limits, namely 1562 and 1561. Again, if the side of a square contain 1000 parts, the diagonal will be the square root of the number 2000000. Since this is an incommensurable number, we seek for its limits by extraction of the square root, namely 1415 the greater limit and 1414 the less limit, or more accurately the greater, and the less; for as we reduce the difference of the limits we increase the accuracy.
7.In place of the unknown quantities themselves, their limits are to be added, subtracted, multiplied, or divided, according as there may be need.
8.The two limits of one quantity are added to the two limits of another, when the less of the one is added to the
