Prob. To furvey a Field, by going round it, at feveral Stations Page. 248 The Conftruction of the Line of Chords, Sines, Tangents and ibid. ibid. ibid. 46. To make a given Angle at the Center or Pole of the primitive perpendicular to another right Circle perpendicular to another oblique Circle perpendicular to another oblique Circle, and to pass thro' a given Point made by an oblique Circle with a right Circle ibid. made by the Interfection of two oblique Circles ibid. 57. To draw an oblique Circle to make a given Angle with a right 63. Any Point being given, as a Pole, to draw its Circle ibid. 68. The Bafe and adjacent Angle given, to find the oppofite Angle 70. The Hypothenufe and Bafe given, to find the Perpendicular to find the Angle oppofite the Bafe 73. The Perpendicular and Angle oppofite given, to find the Bafe 78. The two oblique Angles given, to find the Hypothenuse 81. Two Sides and an Angle oppofite one of them given, to find the ibid. 82. Two Sides and an included Angle given, to find the third Side 278 83. 84. Two Angles and a Side oppofite one of them given, to find the 93. To find the Sun's Place in the Ecliptic 94. To find the Sun's Declination and Afcenfion 95. The Sun's right Afcenfion and greatest Declination given, 97. The Latitude of the Place and the Sun's Declination given, to find the Sun's Altitude, and the Hour of the Day when he is due Eaft 102. The Sun's Declination and his Altitude at Six o'clock given, to find the Latitude of the Place 103. The Latitude of the Place and the Sun's Altitude at Six o'Clock 104. The Sun's Declination and his Azimuth at Six o'Clock given, to find the Latitude of the Place 105. The Sun's Azimuth and Altitude at Six d'Clock given, to find the 107. The Hour of the Day and the Altitude of the Sun when due East given, to find the Latitude of the Place 108. The Hour of the Day and the Altitude of the Sun when in the A SYSTEM O F Practical Mathematics. A Of Vulgar Fractions. RITHMETIC is the Art of numbering. Every Thing, therefore, which may be numbered, is the Subject of Arithmetic. Hence, not only Integers, or whole Things, but their feveral Parts, are brought into arithmetical Computation; fince all Things are, or may be fuppofed, divifible into any Number of equal Parts. Some Things are, for Convenience in Commerce, by Custom divided into Parts, which have a particular Denomination: As a Pound Sterling is divided into 20 Shillings, a Shilling into 12 Pence, and a Penny into 4 Farthings: A Foot is divided into Inches, and an Inch into Quarters and Half-Quarters; and the like of other Things. But it often happens, that Integers are divided into Parts, which have no particular Denomination, but are denominated only from the Number, by which the Integer is divided. Thus any Integer (as a Pound Sterling, for Example) may be fuppofed to be divided into 5, 13, 28, 57, or any other Number of equal Parts ; which can only be denominated from the Number by which the Integer is divided, and called a fifth, a thirteenth, a twenty-eighth, a fifty-feventh Part of a Pound, or whatever is thus divided. In arithmetical Calculations, it often happens, that Integers are divided into different Parts; and a Number of thofe Parts are required to be taken, which generally are lefs than the Number of Parts into which the Integer is divided. Thus a Pound Sterling may be divided into 36 Parts, and it may be required to take 19 of thofe Parts; which are called nineteen Thirty-fixths of a Pound. Again, if a Pound Sterling, or any other Integer, be divided into 17 Parts, and I of those Parts are required to be taken, this is called eleven Seventeenths of a Pound, or whatever elfe is fuppofed to be thus divided. These are what are ufually called Fractions, or the fractional Parts of Things. But, as it is frequently neceffary to bring those fractional Parts into Calculations, a Method has been invented to express them in Figures: The Way of doing which is next to be fhewn. Of the Notation of Fractions, and their feveral Kinds. A Fraction, otherwife called a broken Number, is that by which the Parts of Things are expreffed. Thus, if we were to exprefs three Farthings, a Farthing being the Fourth of a Penny, three Farthings are three Fourths of a Penny; which must be wrote thus, . A vulgar Fraction always confifts of two Parts, that is, two Numbers, fet one over the other, with a Line drawn betwixt them. To exprefs any Number of Inches in Foot-Meafure, as feven Inches, you must put down 7, and 12 under it, with a Line betwixt, as; which is to be read, feven Twelfths of a Foot, an Inch being the twelfth Part of a Foot. If a Foot, a Pound Sterling, or any other Thing, were to be divided into 100 equal Parts, in order to exprefs 32 of thofe Parts by a Fraction, write them thus, , that is, thirty-two Hundredth-Parts of a Foot, Pound, or whatever was fuppofed to be divided. And the Number above the Line is called the Numerator, that below the Denominator: Thus, in the Fraction above-mentioned,, the 7 is the Numerator, and the 12 the Denominator: So in this, five Seventeenths, 5 is the Numerator, and 17 the Denominator. 32 7009 5 The Denominator is fo called, because it denominates or fhews into how many Parts the Integer is divided; and the Numerator is fo called, becaufe it fixes the Number of Parts fignified by the Fraction: Thus, in the Fraction the Denominator 10 fhews that the Integer is divided into 100 32 Parts; |