Decimal Tables of Coin, Weight, and Measure. 80 ,317460 Pints. Decimals. 70 ,27 3 ,005952 60 ,238095 2 ,003968 50 ,198412 1 ,001984 40 ,158730 30 ,119047 TABLE VII. 20 ,079365 MEASURE, 10 039682 Liquid. Dry. 9 035714 8 031746 1 Gullon, 1 Quarter, 7 027 Integer. Pints. Decim. Bush. 6 ,023809 5 ,019841 4, ,5 4 3 4 ,015873 ,375 2 3 2 ,25 ,125 Qt. pt. Decim. Peck. ,09375 3 2 Pints. Decimals. ,0625 2 1 4 ,001984 ,03125 3 ,001488 Decimals. IQ. Pk:.. 2 ,000992 ,0234375 1 3 ,000496 ,015625 2 ,0078125 1 A Hogshead the Integer. Decimals. Pints. ,005859 3 ,003906 2 Gallons. Decimals. ,001953 1 30 ,476190 20 ,317460 10 ,158730 TABLE VIII. ,142857 LONG MEASURE ,126984 1 Mile the Integer. 7 ,ໃນນ 6 ,095238 Yards. Decimals. 5 ,079365 1000 ,568182 4 ,063492 900 ,511364 3 ,047619 800 , 154545 2 ,031746 700 ,397727 1 015873 600 ,340909 12 Decimal Tables of Coin. Weight, and Measure. 500 ,284091 80 ,219178 TABLE X. 400 ,227272 70 ,191781 CLOTH MEASURE. 300 ,170454 60 ,164383 200 ,113636 1 Yard the Integer. 50 ,136986 100 ,056818 40 ,109589 Qrs. the same as 90 ,051136 30 ,082192 Table 4. 80 ,045454 20 ,054794 70 Aails, ,039773 Decimals. 10 ,027397 60 2 ,034091 9 ,02465 ,125 f 50 ,028409 8 ,021918 ,0625 40 ,022727 7 ,019178 30 ,017045 6 ,016-38 TABLE XI. 20 ,011364 5 ,013698 LEAD WEIGHT. 10 ,005682 4 ,010959 9 A Fother the Integer. ,005114 ,008219 8 ,004545 2 ,005479 Hund. Decimals. 7 ,003977 1 ,002739 10 ,512820 6 ,003409 1 Day the Integer. 9 ,461538 ,002841 Hours, | Decimals. 8 ,410256 ,002273 7 ,5 ,358974 ,001704 11 6 ,4583 ,307692 2 ,001136 10 5 ,416 ,256410 1 ,000568 9 4 ,205128 Feet. Decimals. 8 3 ,3 ,153846 2 0003787 7 ,2916 2 1,102564 0001894 6 1 ,25 ,051282 Inches. Decimals. 5 ,2083 Qrs. Decimals. 6 ,0000947 4 2 ,025641 3 ,0000474 3 1 ,012820 1 ,0000158 2 -,083, Pounds. Decimals. 1 ,0416 14 ,0064102 TABLE IX. Min. Decimal. 13 ,0059523 TIME. 30 ,02083 ,0054945 1 Year the Integer. 20 ,013888 11 ,0050366 Months the same a 10 ,006944 10 ,0045787 Pence in the second 9 ,00625 9 ,0041208 Table. 8 ,005555 8 ,0036630 7 ,004861 7 ,0032051 Days. Decimals. 6 ,004166 ,0027472 365 1,000000 ,003472 ,0022893 300 ,821918 ,002777 ,0018315 200 ,547945 ,002083 ,0013736 100 ,273972 ,001388 2 ,0009157 90 ,246575 ,000694 1 ,0004578 ,375 ,125 12 Co Aero VOC EXTRACTION OF THE SQUARE ROOT. EXTRACTING the Square Root is to find out such a num, ber as being multiplicd into itself, the product will be equal to the given number. Rule. First, Point the given number, beginning at the unit's place, then to the hundreds, and so upon every second figure throughout. Secondly, Seek the greatest square number in the first point towards the left hand, placing the square number under the first point, and the root thereof in the quotient; subtract the square number from the first point, and to the remainder bring down the next point, and call that the resolvend. · Thirdly, Double the quotient, and puce it for a divisor on the left hand of the resolvend ; seek how often the divisor is contained in the resolvend (preserving always the unit's place,) and put the answer in the quotient, and also on the right hand side of the divisor ; then multiply by the figure last put in the quotient, and subtract the product from the resolvend; bring down the next point to the remainder (if there be any more) and proceed as before. Roots, 1. 3. 4. 5. 9. SQUARES. 1. 4. 9. 16. 25. 36. 49. 64. 81. 2. 7. 8. 685)3425 3425 2. What is the square root of 1069 29 ? Ans. 327. 3 What is the square root of 2208741 ? Ans, 1506,23+ 4. What is the square root of 7590796 ? Ans. 2756,228+. 5. What is the square root of 36372961 ? Ans. 6031. 9. What is the square root of 22071204 ? Ans. 4698. When the given number consists of a whole number, and decirrals together, make the number of decimals even by adding eyphers to them ; so that there may be a point fall on the unit's place of the whole number. 7. What is the square root of 3271,4007 ? Ans. 57,19 € 8. What is the square root of 4795,25731! Ans. 69,817 +. 9. What is the square root of 4,372594 ? Ans. 2,091 + . 10. What is the square root of 2,2710957 ? Ans. 1,50701 + 11. What is the square root of ,00032754 ? A18. ,01809+. 12. What is the square root of 1,270054 ? Ans. 1,1269 + To extract the Square Root of a Vulgar Fraction. Rule. Reduce the fraction to its lowest terms, then extract the square root of the numerator for a new numerator, and the square root of the denominator, for a new denominator. If the fraction be a surd (i. e.) a number where a root can never be exactly found, reduce it to a decimal, and extract the root from it. EXAMPLES. 2304 5787 EXAMTLES. 13. What is the square root of Ans. Ans. 14. What is the square root of mis 15. What is the square root of 9216. ? Ans. SURDS. 16. What is the square root of 17 ? Ans. ,89802+: 17. What is the square root of 357 ? Ans. ,86602+ 18. What is the square root of 3575 ? Ans. ,933099 +. To extract the Square Root of a Mixed NUMBER. Rule 1. Reduce the fractional part of the mixed number to its lowest terin, and then the mixed number to an improper fraction. 2. Extract the root of the numerator and denominator for a new numerator and denominator. If the mixed number given be a surd, reduce thic fractional part to a decimul, anncx it to the whole number, and extract the square root there. from. 19. What is the square root of 51}? Ans. 75 20. What is the square root of 274 ? 21. What is the square root of 945 Ans. Se 22 What is the square root of 85? Ans. 9,27 + 23. What is the square root of 8;? Ans. 2,9519-+: 24. What is the square root of 6;? Ans. 2,5819 +: To find a mean proportional between any two given numbers. Rule. The square root of the product of the given numbers is the mean proportional sought. 27. What is the mean proportional between 3 and 12 ? Ans. 3x12=36 then ✓ 3636 the mean proportioral. 28. What is the mean proportional between 1276 and 8497 Ans. 1897,4+. To find the side of a square equal in area to any given superficies. Rule. The square root of the content of any giren superfic cies, is the square equal sought Ans. 51 SURDS. EXAMPLES. EXAMPLES 29. If the content of a given circle be 160, what is the side of the square ? Ans. 12,81911. 30. If the area of a circle is 750, what is the side of the square equal ? Ans. 27,38612, The Area of a Circle given to find the Diameter. Rule. As 355 : 452, or, as 1 : 1,273239 :: so is the area : to the square of the diameter :-or, multiply the square root of the area, by 1,12837, and the product will be the diameter. EXAMPLES. 31. What length of cord will be fit to tie to a cow's tail, the other end fixed in the ground, to let her have liberty of eating an acre of grass and no inore, supposing the cow and tail to be 5 yards ? Ans. 6,136 perches. The Area of a Circle given to find the Periphery or Circumference. Rule. As 113: 1420), or, as 1: 12,56637 :: the area to the square of the periphery,-or, multiply the square root of the area by 3,5449, and the product is the circumference. EXAMPLES. 32. When the area is 12, what is the circumference ? Ans. 12,2798. 33. When the area is 160, what is the periphery ? Ans. 44839. Any two sides of a right angled triangle given to find the third side. 1. The Base and Perpendicular given to find the Hypothenuse. Rule. The square root of the sum of ihe squares of the base and perpendicular is the length of the hypothenuse. EXAMPLES 31. The top of a castie from the ground is 45 yards high, and surocomicis inila seminado sio yanits lround; what length must father be io caca troin the outside of the ditch to the top of thie (asile Ans. 75 yariis. |