A Complete Treatise on Practical Mathematics: Including the Nature and Use of Mathematical Instruments: Logarithmic Tables, Trigonometry, Mensuration of Heights and Distances,--of Surfaces & Solids, Land Surveying, Gunnery, Gauging, Artificer's Measuring, Miscellaneous Exercises. With an Appendix on Algebra ... Principally Designed for the Use of Schools and Academies |
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Page xii
... Proportion , Simple Equations , Quadratic Equations , Geometrical Problems , 324 321 337 341 343 348 351 353 ib 355 362 366 - 368 369 370 371 372 • 373 374 385 388 390 392 394 398 402 412 413 418 424 GEOMETRICAL GEOMETRICAL DEFINITIONS ...
... Proportion , Simple Equations , Quadratic Equations , Geometrical Problems , 324 321 337 341 343 348 351 353 ib 355 362 366 - 368 369 370 371 372 • 373 374 385 388 390 392 394 398 402 412 413 418 424 GEOMETRICAL GEOMETRICAL DEFINITIONS ...
Page 17
... proportion- als , and are fo related to the natural numbers , that the addition of Logarithms is equivalent to the multiplication of the corre- fponding numbers ; also , the subtraction of logarithms is the fame as the divifion of the ...
... proportion- als , and are fo related to the natural numbers , that the addition of Logarithms is equivalent to the multiplication of the corre- fponding numbers ; also , the subtraction of logarithms is the fame as the divifion of the ...
Page 30
... proportion ; therefore , the fines , tangents , and fecants of fimilar arches , that is , of equal angles , are as their radii ; confequently , the tabular radius . is to the tabular fine , tangent or fecant of either of the acute ...
... proportion ; therefore , the fines , tangents , and fecants of fimilar arches , that is , of equal angles , are as their radii ; confequently , the tabular radius . is to the tabular fine , tangent or fecant of either of the acute ...
Page 32
... proportions . To find BC . As fiffe C 59 ° 20 ' is to AB , 300 , So fine A 30 ° 40 ′ - · 2.47712 To find AC . 9.93457 As fine C 59 ° 20 ' - 9.93457 is to AB 300 - 2.47712 9.70761 So is rad 90 ° - 10.00000 12.18473 To AC 348.8 ...
... proportions . To find BC . As fiffe C 59 ° 20 ' is to AB , 300 , So fine A 30 ° 40 ′ - · 2.47712 To find AC . 9.93457 As fine C 59 ° 20 ' - 9.93457 is to AB 300 - 2.47712 9.70761 So is rad 90 ° - 10.00000 12.18473 To AC 348.8 ...
Page 33
... proportions . To find AB . To find AC . As fine A 53 ° 3 ' - Is to BG 4876 , So fine C 36 ° 57 ′ . · 3.68806 9.90263 As fine A 53 ° 3 ′ is to BC 4876 · 9.77896 So is rad . 90 ° 9.90263 3.68806 10.00000 13.46702 To AC 610.1 - 3.78543 To ...
... proportions . To find AB . To find AC . As fine A 53 ° 3 ' - Is to BG 4876 , So fine C 36 ° 57 ′ . · 3.68806 9.90263 As fine A 53 ° 3 ′ is to BC 4876 · 9.77896 So is rad . 90 ° 9.90263 3.68806 10.00000 13.46702 To AC 610.1 - 3.78543 To ...
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Common terms and phrases
abfciffa acres againſt alfo alſo altitude amplitude axis bafe baſe becauſe breadth centre chain chord of half circle circumference Co-fec Co-tan column cone conjugate cube defcribe dift diſtance divide divifor elevation Engliſh equal Euclid EXAMPLE fame fecond fegment fhall fimilar find the area find the folidity firſt fquare root fquare yards fruftum ftraight line fubtract fuch fuperficies furface girt given greateſt half the arch height horizontal houſe hypothenufe inftrument laft acquired velocity laſt lefs logarithm malt bufhels meaſure obferved off-fets oppofite ordinate parabolic perpendicular plane Plate quantity quotient rectangle Required the area Required the content Required the folidity rhombus right angles RULE Secant Secant Co-fec ſpace ſphere ſpindle ſquare ſteeple Suppofe tangent theodolite theſe thickneſs tranfverfe trapezium triangle triangular uſed verfed whofe diameter whofe fide whofe length whoſe wine gallons
Popular passages
Page 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.
Page 115 - 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.
Page 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 232 - E, is equal to twice as many right angles as the figure has sides, less four right angles.
Page 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.
Page 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.
Page 372 - 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...
Page 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.
Page 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...
Page 395 - 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...