A Synopsis of Practical Mathematics: Containing Plain Trigonometry, Mensuration of Heights, Distances, Surfaces, and Solids ... [surveying of Land, Gauging, Navigation, and Gunnery.] With Tables of the Logarithms of Numbers, and of Sines and Tangents. For the Use of Schools and Men of BusinessW. Smellie, 1771 - 160 pages |
Table des matières
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Autres éditions - Tout afficher
A Synopsis of Practical Mathematics: Containing Plain Trigonometry ... Alexander Ewing Affichage du livre entier - 1799 |
A Synopsis of Practical Mathematics: Containing Plain Trigonometry ... Alexander Ewing Affichage du livre entier - 1799 |
Expressions et termes fréquents
alfo altitude amplitude angle ABC angle ACB angle BAC angled triangle ABC anſwer bafe baſe becauſe Cafe circle circumference cofine compaffes courfe courſe defcribe diameter Diff diſtance divide ecliptic elevation Engliſh equal equator EXAM failed fcale fecant fecond fegment feven fhip fide AC fides AB field figures find the angles find the area find the folidity firſt folid content fome fouth fquare feet fquare links fquare root fruftum ftations fubtract fuch fun's fuperficies fuppofe furface given right line globe greateſt half fum height horizon inftrument length line of chords logarithm longitude meaſure the angle meridian miles Multiply muſt oblique angled triangle oppofite parallel parallelogram perpendicular plain triangle pole polygon PROB proportion quantity quotient radius regular polygon right angled triangle roods ſcale Sine ſquare Tan.Com Tangent thefe theſe TRIGONOMETRY veffel weft whofe whoſe yards
Fréquemment cités
Page 154 - And in division, subtract the logarithm of the divisor from the logarithm of the dividend, the remainder is the logarithm of the quotient.
Page 155 - Rule. Multiply the Logarithm of the given number by the Index of the proposed power, and the product will be the Logarithm, whose natural number is the power required.
Page 118 - ... cuts the horizon in the eaft and weft points. 36. An azimuth circle is fuppofed to pafs through the fun, moon, or any ftar which appears above the horizon.
Page 116 - ... the ecliptic, reckoned on the circle of longitude paffing through the ftar. 24. Longitude of any ftar in the heavens, is an arch of the ecliptic between the vernal equinox and the circle of longitude paffing through the ftar, reckoned in the order of the figns. 25. Declination, is the difb.nce of the fun, or any ftar, north or fouth from the equator, reckoned on the meridian.
Page 40 - ... different points, either (1) the vertex of each of the triangles ABC, ABD must be outside the other triangle, (2) the vertex of one triangle must be inside the other, or (3) the vertex of one triangle must be on a side of the other. (1) First let the vertex of each triangle be without the other. Because AD is equal to AC, the angle ACD is equal to the angle ADC. (Prop. 5.) But the angle ACD is greater than the angle BCD, and the angle BDC is greater than the angle ADC : therefore the angle BDC...
Page 76 - The circumferences of circles are to each other as their diameters, and their areas are to each other as the squares of their diameters.
Page 155 - To find the arithmetical complement of a logarithm -, begin at the left hand, and write down what each figure wants of 9, and what the laft fignificant figure wants of ю ; fo the arith. сотр. of 2.6963564 is 7.3036436. 11. To raife a number to any power, by logarithms.
Page 99 - To find the folid content of a cone, the diameter of its bafe and height bïing given. Fig. 77. Becaufe every cone is the third part of a cylinder of the fame bafe and altitude, Multiply the area of its bafe by one third part of its height ; the product is the foiidity.
Page 147 - ... 64). Similarly, the difference of any two logarithms is the logarithm of the quotient of the numbers; a multiple of any logarithm is the logarithm of the corresponding number raised to the power of the multiple, eg, 8 (= 4 x 2) is the logarithm of 256 (= 10a), and a submultiple of a logarithm is the logarithm of the corresponding root of its number.
Page 130 - CASE i. Given the latitudes and longitudes of two places, to find their bearing and diftance. EXAM. Required the courfe and diftance from Cathnefs-point, in the nbrth of Scotland, in latitude 58° 46' N, longitude 3° 17