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To measure an Irregular Body another Way, more

exactly To find the side of a Cube equal to any given

Solid

152

153

The CONIC SECTIONS

154

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164

The QUADRATURE; OR, MENSURATION OF

SURFACES ARISING FROM THE Sections 159

OF A CONE
To find the Foci of any Ellipfis

159 To delineate an Ellipfis

160 To find the Circumference of an Ellipfis

161 To find the Area of an Ellipfis

162 To find the Area of a Segment of an Ellipfis

163 To find the Focus of a Parabola To delineate a Parabola

165 To find the Length of an Arch of a Parabola 166 To find the Area of a Parabola

167 To find the Area of a Frustum of a Parabola

168 Of an Hyberbola

169 To delineate an Hyperbola

170 To find the Length of an Arch of an Hyperbola 172 To find the Area of an Hyperbola

173 The CUBATURE; OR, MENSURATION OF SOLIDS ARISING FROM

THE SECTIONS
OF A CONE
To find the Solidity of a Spheroid

174 To find the Solidity of the Segment of a Spheroid 176 To find the Solidity of the Middle Zone of a Spheroid 177 To find the Solidity of a Parabolic Conoid

178 To find the Solidity of a Frustum of a Parabolic Conoid

179 To find the Solidity of a Parabolic Spindle

180 To find the Solidity of the middle Zone of a Parabolic

Spindle
To find the Solidity of an Hyperbolic Conoid

182 To find the Solidity of the Frustumn of an Hyperbolic Conoid

183

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174

181

219

220

221 222

PAGE To find the Area of any Space of Archimedes' Spiral 212 To find the Area of a Cycloid

213 To find the Area of a Segment, or Part of a Sector of a Circle

214 To describe a Parabola, by having only the Base and Height given

215 To find the Length of the Transverse and Conjugate Axis of an Hyperbola

217 To delineate an Hyperbola, the Transverse and Con

jugate Diameters being given To find the Solidity of a Circular, Elliptical, Parabo

lical, or Hyperbolical Spindle
To find the Solidity of a Frustum, or Segment of an

Elliptical, Parabolical, or Hyperbolical Spindle
To find the Sólidity of a Wedge
To cut a Tree so that the two Parts measured separately
shall produce more than the whole Tree

223 To cut a Tree so that the Part next the greater End may measure the most possible

224 To determine, geometrically, the Point in a given

Right Line, from which the Sum of the Diftances
of two Objects shall be the least possible

225 The Nature of Cube Numbers exemplified in measuring Stacks of Hay

226 To find the Difference of the Areas of Isoperimetrical Figures

227 To find the Side of a Cubic Block of Gold, which

being coined into Guineas, would pay off the
National Debt

229 To find what Annuity would pay off the National

Debt of 250 Millions in 30 Years, at 4 per Cent.
Compound Interest

230 Of Magic Squares

231 To Square the Circle

233 To raise the Earth according to the Proposal of the

great Geometrician Archimedes of Syracuse 238 Plato, a celebrated Greek Philofopher, who Alourished about 350 Years before Christ, was used, in his Lectures, to illustrate and demonstrate to his Pupils the Truth of his Propositions by Geometry; and EUCLID, who lived about fourscore Years after him, being educated in Plato' School, is said to have compiled his whole System of Geo metrical Elements only in Reference to Applications of tha Kind. But now, the Utility of Geometry extends to everi Art and Science in Human Life.

E R R A T U M. Page 73, line 7, after the Period, read, “ With the fame Extent, a one Foot in b, make a Mark at co'

THE YOUNG

Geometrician's Companion.

D E CI M A L·

ARI TH ME T I C.

T

HIS is a particular Kind of Arithmetic, which

enables us to treat Fractions as whole Numbers; and it is of the greatest Use in all parts of Mathematical Learning. It receives its Name from Decem (Latin for Ten), because it always supposes the Unit or Integer, let it be what it will, whether i Pound, 1 Mile, i Gallon, to be divided into ten equal Parts, and each of those into 10 more, and so on, as far as we please,

Definitions.

A Fraction is a Number expreffing fome Part or Parts of an Unit or Integer : So the Half, a Third, or Tenth Part of any Thing are Fractions.

Every Fraction consists of two Numbers, the Numerator, and the Denominator. The Denominator shews into how many Parts the Unit or Integer is divided; and the Numerator is the Number expressing how many of those Parts are intended by the Fraction.

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