EXAMPLES. 1- What is the squared Biquadrate of 48? 281.9280429056. 2 What is the square biquadrate root of 7213895789838336? 3 What is the square biquadrateroot of 28179280429056 ? 4 What is the square biquadrateroot of 472769874482845188096 ? Ans. Ans. 96. Ans. 48. t Ans. 384. OF THE CUBED CUBE ROOT. Q. WHAT is a Cubed-Cube? Cube. A. Any number involved nine times is a Cubed Ans. 384. 5. of 18154363180141255228864? OF THE SQUARE SURSOLID ROOT. Q. WH A. Any number involved ten times, produces a Squared Sursolid. EXAMPLES. 1. What is the Squared Sursolid Root of 64925062108545024? 2. What is the Squared Sursolid Root of 66483263599150104576? 3. What is the Squared Sursolid Root of 69743754611742420055883776 P Ans. 48. Ans. 96. Ans. 384. 3. OF THE THIRD SURSOLID ROOT. Q. WHAT is a Third Sursolid? A. Any number involved eleven times, produces a third Sursolid. OF THE SQUARED SQUARE CUBE ROOT. Q. WHAT is a Squared Square Cube ? A. Any number involved twelve times, produces a Squared Square Cube. EXAMPLES. 1. What is the root of this Squared Square A. 48. Cube 149587343098087735296? 2. What is the root of this Squared Square Cube 612709757329767363772416 P A. 96. 3. What is the root of this Squared Square? A. 384. Cube 10279563944029090291760398073856 ? A GENERAL RULE FOR EXTRACTING THE ROOTS OF ALL POWERS. 1. PREPARE the given number for extraetion, by pointing off from the unity place, as the root required di reets. 2. Find the first figure in the root by your own judgment, or by inspection into the table of powers. 3. Subtract it from the given number. 4. Augment the remainder by the next figure in the given number, that is by the first figure in the next point, and call this your dividend. 5. Involve the whole Root, last found, into the next inferior power to that which is given. 6. Multiply it by the index of the given power, and call this your divisor. 7. Find a quotient figure by common Division, and annex it to the root. 8. Involve all the root thus found, into the given power 9. Subtract this power (always) from as many points of the given power as you have brought down, beginning at the lowest place. 10. To the remainder bring down the first figure of the next point for new dividend. 11 Find a new divisor as before, and in like manner proceed till the work is ended. 487 X 487 X 487115501303 Subtrahend. ? What is the Biquadrate root of 56249134561 P 487 X 487 X 48756249134561 485308416 Subtrahend 4442368 Divisor Sub. Note. This Ceneral Rule I receive from my worthy Friend, William Montaine, Esq. F. R. S and teacher of the Mathematics at Shad-Thames, ૨. OF SIMPLE INTEREST. WHAT particular Letters are used here? A. These: P, any Principal. T, the time. R, the ratio of the rate per cent. Q. What is the ratio ? A. It signifies only the simple interest of 11 for one year, at any proposed rate of interest per cent, and is thus found, 100 6: 1: 0.06 100 5 1 : 0.05 A TABLE OF RATIONS. Rate per Ct. Ratio. Rate per Ct. Ratio. Q. When P, T and R are given to find A, how is it discovered? A. Thus ptr+p=A. Note. Any quantity of Letters put together like a word, denote continual Multiplication. per cent per annum ? EXAMPLES. 1. What sum will 5677 108 amount to in 9 years, at 6 Ans. 873. 19s. 2. What will 508l 148. amount to in 1 year at 5 per cent. per annum ? Ans. 5341 2s 8d 1. 6 qrs. 3. What will 600l 14s. amount to in 10 years, at 4 per cent. per annum ? Ans. 8717 os. 3d. 2.4 qrs. 4. What will 4000l, amount to in 5 years, at 34 per cent. per annum? Ans. 47001. Note. When the time given does not consist of whole years, then reduce the odd time into Decimal parts of a year. And unless such parts of a year chance to be or of a year, the best way will be to reduce the odd times into days, and then work with the Decimal parts of a year, that are equivalent to those days. A Table for the ready finding the Decimal Parts of a year equal to any Number of Days, or Quarters of a Year. Days Dec. Pts. | Days | Dec. Pts. | Days | Dec. Pis. Note. When the true Number of Days cannot be found at one view in this Table, then both them and their Decimals must be taken out of the Table at twice or thrice, as their Number requires, and added together. So the Decimal Parts of a year-236 days are thus found, 200 .547945 6=.016438 EXAMPLES. 5 What will 72001 amount to in 6 years, at 5 per cent. per annum? Ans. 9540l. 6 What will 1110 18s amount to in 123 years at 5 per cent. per annum? Ans. 18197 is 11d 2.8qrs. 7 What will 280l 10s amount to in 3 years and 148 days, at 5 per cent. per ann.? Ans. 3281 5s 2d 3.58+qrs. 8 What will 1967 amount to in 189 days, at 4 per cent. Ans. 200l is 2d 1.23+qrs. per ann. ? CASE 2. Q. When A. T. & R. are given to find P, how is it discovered? 1 I demand what principal will amount to 8731 19s in 9 years, at 6 per cent. per ann.? Ans. 567 10s. 2 1 demand what principal will amount to 5341 2s. 8d 1.6 qr. in one year, at 5 per cent. per ann.? Ans. 5087 14s. 3 I demand what principal will amount to 9540l in 64 years, at 5 per cent. per ann. ? Ans. 72001. 4 1 demand what principal will amount to 1819/18 ild 2.8 qrs. in 122 years, at 5 per cent. per ann.? Ans. 1110/ 18s. |