COROLLARY XXI. 299. The Circumference of the Earth upon this Suppofition equals 69 × 360o = 25000 Miles nearly; as was found by the learned Picard, and after him by the famous Coffini; which is but 20 Miles lefs than what was found by our Country-man Mr. Norwood upon a lefs advantagious Experiment. DEFINITION XVIII. 300. The leaft Denomination of Superficial Meafure is a Square Inch In.s i. e. an Inch in Length and Breadth. In. The Table of Superficial Measure. 144= 1 Foot Square. 1296= 9 F= 1 Yard Square. 3600= 25= 22= I Pace Square. 89 39204 272 304 10,= 1 Perch, or Pole Square. 1568160=10890=1210= 435 401 Rood. 6272640=43560=4840=1742-4=160=4=1 Statute Acre. DEFINITION XIX. 301. Because an Acre or 160 Square Perches = 43560 Square Feet is equal to 40 Perches or 40 X 16 = 660 Feet in Length, and 4 Percbes or 4×16 =66 Feet in Breadth: Therefore in Land Meafure there is commonly used a Chain of 66 Feet or 22 Yards Long; every 10 of which in Length and I in Breadth (i. e. every 10 Square Chains) makes an Acre. And this Chain is fubdivided into 100 Links of 7.92 Inches each, according to which Sq. Chains, Sq. Links, Acre, Roods, Perches Square. = 4 = 160 DEFINITION XX. 40 I. 302. Measures of Capacity are fuch as are of three Dimenfions; viz. Length, Breadth, and Thickness, Height or Depth: Of which there are especially four Sorts used in Britain, viz. Corn, Beer, Ale, and Wine Meafure: The leaft Denomination to all which is called a Cubic Inch, i. e. an Inch in Length, Breadth, and Thickness. DEFINITION XXI. 303. In the Table of Corn Measure, 1 Gallon = 268,8 Cubic Inches, and the leaft Denomination is a Pint, Pt. 512 256 64= 32= 8= 4= 2= 1 Seam, Raft, or Quarter. 3072=1536=384=192=48=24=12= 6= 1 Wey. 5120=2560=640=320=80=40=20=10=1=1 Last. 306. In Wine Meafure the Gallon equals 231 Cubic Inches, by which are measured all Wines, Brandies, Spirits, Mead, Perry, Cyder, Vinegar, Oyl, Honey, &c. The Gills, Pints, Quarts. The TABLE. 16 = 8 = 4 = 1 Gallon as before. 18= 18 1 Rundlet. 314=1= 1 Barrel. 42=2=1= 1 Tierce. 63=31= 2=1= 1 Hogfhead. DEFINITION XXV. 307. The leaft Denomination of any Part of Time is a Second, from whence is formed the following Table of Time: 2360587=39343+7=655+43+7=27+7+43+7=1 Periodical Month, or the Time which the Moon takes up in finishing her Courfe round the Earth. 29+12+44+08=1 Mean Synodical Month or Lunation, i. e. the mean Time between Conjunction and Conjunction. The Calendar or Civil Month confifts of fometimes 30 Days fometimes 31; and one Month, viz. February, of 28 or in Leap-Year 29 Days. D. H. " 365+5+48+57=1 Solar or Tropical Year, i. e. the Time which the Sun takes up in finifhing its apparent Course thro' the 12 Signs of the Zodiack. D. H. " 365+6+9+14=1 Syderial, Anomalistical, or Periodical Year; the Space of Time which the Sun takes up in finishing its apparent Course round the Earth. The Civil, Julian, or Calendar Year, is the Space of 12 Calendar Months, or of 365 Days 6 Hours; or it is the Space of 365 Days every Common Year, and of 366 every Fourth Year, which is therefore called Biffextile or Leap-Year, becaufe of the Day added. DEFINITION XXVI. 308. The Golden Number, Cycle of the Moon, or Metonic Cycle (fo called from itis Author Meton) is a Period of 19 Julian Years, which is fuppofed to be be equal to 235 Lunations, fo that every new and full Moon is computed to return to the fame Day of the Month it was 19 Years before, but with the Errour of about 1 Hour in Point of Defect. The Beginning of this Cycle was the Year before Chrift. DEFINITION XXVII. 309. The Cycle of the Sun is the Space of 28 Years, in which Time all the Days of the Year return to the fame Day of the Week that they were 28 Years before. The Beginning of this Cycle was 9 Years before Chrift. CHAP. IV. Of the Addition and Subtraction of Polynomial NUMBERS. PARTITION VIII. DDITION and Subtraction of Polynomial Numbers is either tracted are fuch. PROBLEM I. 311. To add two or more given Homogeneous Polynomes into one Sum. Effection. Pre. 1. Set all the Homogeneous Figures which belong to each given Number in the fame Column one under another (In. 67.) Pre. 2. Draw a Line beneath all. Pre. 3. Begin at the lowest Figure in the firft Column to the Right-hand, and add up all the Figures in that Column marking all the Tens. Pre. 4. Set down the Remainder above all the Tens in the firft Column. Pre. 6. Thus continue doing thro' all the Columns. Pre. 7. And because in fumming up the laft Column, there remains no other Column for the Tens to be added to; therefore they are to be fet down by themselves: And the Number thus found will be the Sum re quired (In 35.) Q. E. E. Ex. gr. Ex. gr. Let it be required to find the Sum of the given Numbers 4037. 654+7956.508684.097+5932.630. First fet down the Numbers as in the 4037.654 b 0684.097 = d Margin, then, beginning at the lowest Figure in the firft Column to the Right hand, which is here the Fractional Place of Thoufandths, fay 7 and 8 is 15, and 4 is 19, or 7+8+4=19=10+9, fet down 9 and carry 1 for the 10; 1+3+9+5=18, fet 18610.889 = b + c + d + f. down 8 and carry 1; 1+6+5+6=-18, fet down 8 and carry ; 1+2+4 +6+7=20, fet down o and carry 2; 2+3+8+5+3=21, set down i and carry 2; 2+9+6+9=26, set down 6 and carry 2; 2+5+7+4=18, which fet down by Precept 7. Therefore the Sum required is 18610.889. i. e. 18 Thousand, 6 Hundred, and Ten, with 889 Thousandth Parts. PROBLEM II. 312. To fubtract a leffer given Pure Polynome from a greater given one. Effection. 1. Place all the Homogeneous Figures in the fame Column one beneath another (In. 67.) 2. Draw a Line beneath all. 730.25 = c 3. Begin at the lower Figure in the firft Column to the Right-hand, and subtract every lower Figure in each Column from its refpective one above. 4. When the upper Figure is leffer add 10 to it, in fuch Cafe always obferving either to take an Unit from the next upper Figure to the Left-hand, or which is the fame Thing add an Unit to the next lower Figure (In. 68.) And the Number thus found will be the Difference required. Q.E. E. Ex. gr. Let it be required to take the Number 730.25 from the Number 940.18. First fet down the Numbers as in the Subtrahend 940.18 = b Margin, then, beginning at the lower Figure Minuend in the first Column to the Right-hand, fay 5 from 8 leaves 3 to be fet down under the first Column; 2 from 1 I cannot take, but 2 from 10+1=11 leaves 9 to be fet under the fecond Column; then for the 10 that I added to the upper Figure in the fecond Column I add to the lower Figure in the third Column, thus 0+1=1, and proceed faying 1 from o I cannot, but I from 10+0=10 leaves 9, which I fet under the third Column; then I that I add to 3 in the fourth Column for the 10 added to o in the third makes 4, 4 from 4 leaves o, which I fet under the fourth Column: Laftly, 7 from 9 leaves 2, which I fet down under the laft Column. And the Remainder is found to be 209.93. PROBLEM III. Remainder 209.93 = b 313. To add together two or more Mixed Polynomes into one Sum. F Effection. |