...contained five times in unity, and nine times in | . is the common measure of unity and the fraction |, and the relation these quantities have to each other...exactly, at the same time, both this root and unity. In order to denote, in general, that a root is to be extracted, whether it can be exactly obtained...

...exactly determined, but approximations to it may be made continually, as will be seen hereafter. 132. The square root of a number, which is not a perfect square, is called a surd, irrational, or ineommensu* rable number. - 133. \Ve will now consider numbers, which...

...measure with unity, we say that these quantities are commensurable with unity, or simply that they arc commensurable ; and since their relations or ratios,...incommensurable or irrational, because, as it cannot he represented by any fraction, into whatever number of parts we suppose unily to bo divided, no one...

...we cannot exactly assign, but to which we can approach continually, as we shall see shortly. 1 32. The square root of a number which is not a perfect square, is called a surd, irrational, or incommensurable number, 133. Let us proceed to numbers which have more...

...hypothesis. What analogy can there be between ' the Name of . a Man, and the Number of his Name,' and the Square Root of a Number which is not a perfect Square ? A greater perversion of Mathematical Knowledge, as connected with the Holy Scriptures. could not...

...root of 994009. 4. To find the square root of 85678973. 0. To find the square root of 67812675. 118. The square root of a number which is not a perfect square, is called incommensurable or irrational, because its exact root cannot be found in terms of the numerical...

...and Examples ..... 262 1 36 Tests for the Discovery of Square Numbers ... 264 138 Approximation to the Square Root of a Number which is not a perfect Square ----.. 265 139 Extraction of the Square Root of a Vulgar Fraction - - 267 140 Extraction of the Square...

...will the square root of a number comprised of one or two figures contain ? Between what numbers will the square root of a number which is not a perfect square be found -' Between what numbers will the square root of 96 be found ? y.;-, . •/37T -/24? 221* Every...

...will the square root of a number comprised of one or two figures contain ? Between what numbers will the square root of a number which is not a perfect square be found ? Between what numbers will the square root of 96 be found ? ,/Jjfj N/37? >/24? 221* Every...

...number; then (a+l)2 — a2=«2+2a-(1 — a2=2o+l=a+(a+l), which was to be proved., Next, to extract the square root of a number, which is not a perfect square, to a degree of approximation within a given fraction. cin. Let a=the number ; then a ntay be put under...