# A Complete Treatise on Practical Mathematics: Including the Nature and Use of Mathematical Instruments ...

G. G. J. & J. Robinson, 1792 - 431 „š «Š’›Õ«

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 Dersitions 4 Triangles conſtructed and meaſured by the Scale 17 Rightangled Trigonometry 27 To gauge Surfaces 324 32 Obliqueangled Trigonometry 37 Menſuration of Heights and Diſtances 46 To find the Diameter of the Earth by Trigonometry 54 Heights and Depths eſtimated by falling Bodies 63
 Of the Ellipſe and its parts 2 217 Of the Hyperbola and its parts 223 LAND surveying 245 Of dividing or laying out of Ground 273 GUNNERY 279 Oblique Caſes 290 Specific Gravity 303 Of Balls and Shells 3 321

 Square 64 117 Duodecimals II 4 117 To find the Length or Breadth of a given Parallelogram 121 To find the Area of a Triangle I 22 129 To find the Area of an irregular Polygon 135 To find the Area of the Cycloid 162 To find the Secant and Cofecant of an Arch 169 To find the Solidity of a Cube I 74 175 To find the Superficies of the Fruſtum of a Cone 180 To find the Solidity of the Fruſtum of a Cone or Pyramid 187 To find the Superficies of any Zone 194 To find the Solidity of a circular Spindle 2O I 203 To deſcribe an Ellipſe 209
 Inching Tuns and Coolers 337 To gauge a Copper with a riſing Crown 343 To gauge malt 35 I 351 The common Method exploded 359 Maſonwork 366 Glazierswork 372 ALGEBRA 385 Multiplication 392 Involution 398 Proportion 412 Quadratic Equations 4 18 418 Geometrical Problems 424

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«Š’›Õ… 27 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.Ģ
«Š’›Õ… 129 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.Ģ
«Š’›Õ… 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.Ģ
«Š’›Õ… 254 - E, is equal to twice as many right angles as the figure has sides, less four right angles.Ģ
«Š’›Õ… 1 - ... common to the two triangles AFE, BFE, there are two sides in the one equal to two sides in the other, each to each ; and the base EA is equal to the base EB ; (i.Ģ
«Š’›Õ… 38 - BG; that is, the fum of the fides is to their difference, as the tangent of half the fum of the angles at the bafe to the tangent of half their difference.Ģ
«Š’›Õ… 394 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained...Ģ
«Š’›Õ… 38 - AB the greater side for a distance, let a circle be described, meeting AC, produced in E, F, and BC in D; join DA, EB, FB; and draw FG parallel to BC, meeting EB in G. The angle EAB (32.Ģ
«Š’›Õ… 38 - ACB (32. 1.) is equal to the angles CAD and ADC, or ABC together ; therefore FAD is the difference of the angles at the...Ģ
«Š’›Õ… 417 - TO divide a given ftraight line into two parts, fo that the rectangle contained by the whale, and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given ftraight line; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB...Ģ