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Section the eighth treats of surveying Harbours, Shoals, Sands, &c. Section the ninth treats of Levelling, adapted to the surveying of roads and hilly ground, with promiscuous questions. Section the first (Part the Third) contains the Astronomical methods of finding the Latitude, Variation of the Compass, &c. with a description of the instruments used in these operations. Section the second contains a description of the instruments requisite in Astronomical Observations. Section the third shows how to find the Latitude by the Meridian Altitude of the Sun. Section the fourth shows how to find the Variation of the Compass, with a description of the Azimuth Compass, and its use. In this edition is introduced a new set of accurate Mathematical Tables. Truth calls upon me to acknowledge, that the methods of calculation herein set forth, got their rise from those of the late Thomas Burgh, Esq.” who first discovered a universal method for determining the Areas of right-lined figures, and for which he obtained a reward of twenty thousand pounds sterling, from the Irish Parliament. I hope, therefore, it cannot be construed as an intention in me to take from his great merit, when I say, that the methods herein contained are much more concise and ready than his.
* This method, with very little alteration and improvement, in this country, is usually called the Pennsylvania Method of Calculation.-Ed,
+ signifies plus, or addition.
— - - minus, or subtraction. × or . - multiplication. -- - - division. - proportion. = - - equality. v - - square root. W - - cube root. &c. an - - difference between two numbers, when it is not
known which is the greater.
5 + 3, denotes that 3 is to be added to 5. 6–2, denotes that 2 is to be taken from 6. 7 × 3, or 7.3, denotes that 7 is to be multiplied by 3. 8 + 4, denotes that 8 is to be divided by 4. 2: 3: : 4: 6, shows that 2 is to 3 as 4 is to 6. 6 + 4 = 10, shows that the sum of 6 and 4 is equal to 10.
v. 3, or 3%, denotes the square root of the number 3.
W 5, or 5°, denotes the cube root of the number 5.
7°, denotes that the number 7 is to be squared.
8°, denotes that the number 8 is to be cubed. Etcetera.
su R v EY ING.
THE word Surveying, in the mathematics, signifies the art of measuring land, and of delineating its boundaries on a map.
The Surveyor, in the practice of this art, directs his attention, at first, to the tracing and measuring of lines; secondly, to the position of these lines in respect to each other, or the angles formed by them; thirdly, to the plan, or representation of the field, or tract, which he surveys; and fourthly to the calculation of its area, or superficial content. When this art is employed in observing and delineating Coasts and Harbours, in determining their variation of the Compass, their Latitude, Longitude, and soundings, together with the bearings of their most remarkable places from each other, it is usually denominated Maritime Surveying. This branch of Surveying, however, demands no other qualifications than those, which should be thoroughly acquired by every Land-Surveyor who aspires to the character of an accomplished and skilful practitioner. Surveying, therefore, requires an intimate acquaintance with the several parts of the Mathematics which are here inserted as an introduction to this treatise.
Containing Decimal Fractions, Involution and Evolution, the JNature and Use of Logarithms, Geometry and Plane Trigonometry.
If we suppose unity or any one thing to be divided into any assigned number of equal parts, this number is called the denominator; and if we choose to take any number of such parts less than the whole, this is called the numerator of a fraction.