An intire system of arithmetic: or, Arithmetic in all its parts. Containing I. Vulgar; II. Decimal; III. Duodecimal; IV. Sexagesimal; V. Political; VI. Logarithmical; VII. Lineal; VIII. Instrumental; IX. Algebraical. With the arithmetic of negatives, and approximation or converging series ... With an appendix, shewing the mensuration of ... superficies and solids / Written by Edward Hatton gent.

Edward Hatton

Date:: 1721

Credit: An intire system of arithmetic: or, Arithmetic in all its parts. Containing I. Vulgar; II. Decimal; III. Duodecimal; IV. Sexagesimal; V. Political; VI. Logarithmical; VII. Lineal; VIII. Instrumental; IX. Algebraical. With the arithmetic of negatives, and approximation or converging series ... With an appendix, shewing the mensuration of ... superficies and solids / Written by Edward Hatton gent. Source: Wellcome Collection.

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Defin: This Figure only differs from that under Prof. 1. Seel. 1. of Chap. 2. inafmuch as that hath a Circle, this hath an Ellipfis for its Bale : fo that to meafure it, Rule. Multiply the Bafe found as per Prop. 3. Sell. 2. Chap. 1. by the Length, and that Produd is the Anfwer. Example. Admit the Latus tranfverfum (as It, Fig.’]. Plate C.) by c dz=. the Diameter Conjugate, (i. e. fuppofe It = 15.34, ancf cd~ 12.28) the Area is™ 147.25, which multiply, cl by the Length = i.Sri, the Anfwer is — 272.45. Prop. 4. ‘To find the folid Content of the Sphereoid. Defin. This Figure is generated by the Rotation of the Semi-Ellipfis round its Axis, or Latus tranfverfum; and dis by fome called the Prolate Sphereoid, to diftinguifh it from that which is generated by the Rotation of a Semi-Ellipfis, which turns round its Dia¬ meter Conjugate, and is called an Oblate Sphereoid, (of which Figure, dis averted by the moft Learned, our Earth is, the Dia¬ meter at the Equator being greater than between the Poles.) This Prolate Sphereoid is 2 Thirds of a Cylinder, whofe Bafe’s Diameter is = the greateff Diameter of the Sphereoid, and its Altitude = the Latus tranfverfum of the Ellipfis. Rule. Multiply the Area of a Circle, whofe Bafe is the Conjugate Diameter, (or here the greateft Diameter of the Sphereoid) by the Length, and 2 Thirds of the Produd is the Content of the Sphereoid. Example. The Diameter in the middle — 14-32, as c d, Fig. 7. the * Area of that Circle 161.05 6, which multiplydi in the Length ltz=zi4, gives 200.48 ; 2 Thirds of which = 133.<55, the Anfwer. * Prop. 5. To find the Solidity of the Hyperbolic Conoid. Defin. This Figure is generated by the Rotation of the Semi-Hyper¬ bola (z, hr i) Fig. 9. round the Abfciffa z, i ; which formeth the Hyperbolic Conoid h r i nz, h. Ride. The Latus tranfverfum = i 0, multiply dl by 6 ; more the Axis or the Abfciffa i z, multiply M by 6 is — the Divifor. idly. Multiply (h a i s n z, h) = the Content of the Cylinder (whofe - Diameter is equal to the whole Ordinat h n, and its Length = the Abfciffa z, 1) in 3 times the Latus tranfverfum, more 2 times the Abfciffa, and that Redangle is = a Dividend,* which di¬ vided, there arifeth the Quotient, which is the Solidity required. Example. The whole Ordinat (or Diameter) hn= 3.51, the Ab- - feifs or Axis i%> = ha =2.43, and. the Latus tranfverfum i 0 < = 2.id. The e

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