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 AcademiesBell and Bradfute, 1792 - 431 Seiten |
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Seite 29
... fimilar , CH : CD ( = CE ) :: CE : CG . Hence , In words , The radius is a mean proportional between the co - fine and fecant of any arch . Corol . 3. Because the triangles BKC , GCD are fimilar , GD : DC ( = CB ) :: CB : BK . Hence ...
... fimilar , CH : CD ( = CE ) :: CE : CG . Hence , In words , The radius is a mean proportional between the co - fine and fecant of any arch . Corol . 3. Because the triangles BKC , GCD are fimilar , GD : DC ( = CB ) :: CB : BK . Hence ...
Seite 30
... fimilar arches of the fame circles will be in the fame 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 ...
... fimilar arches of the fame circles will be in the fame 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 ...
Seite 37
... fimilar , and confequently , BC is to CA , as BE is to AD ; that is , the fides are in the fame proportion as the fines of the oppofite angles THEO- THEOREM II . In any plane triangle , the fum Oblique-angled Trigonometry,
... fimilar , and confequently , BC is to CA , as BE is to AD ; that is , the fides are in the fame proportion as the fines of the oppofite angles THEO- THEOREM II . In any plane triangle , the fum Oblique-angled Trigonometry,
Seite 60
... fimilar experiment , the velocity of running waters may be computed . PROBLEM VIII . Heights or depths may be estimated from the velocities acquired by fal- ling bodies , and the spaces fallen through in given times , or from the time ...
... fimilar experiment , the velocity of running waters may be computed . PROBLEM VIII . Heights or depths may be estimated from the velocities acquired by fal- ling bodies , and the spaces fallen through in given times , or from the time ...
Seite
... fimilar triangles , ES : SB :: as BA : AG ; but if the index cut the right fide of the square K , it will be BR : RK :: BA : AF . In either of these cafes , the distance required may be found by the rule of three * . Perpendicular ...
... fimilar triangles , ES : SB :: as BA : AG ; but if the index cut the right fide of the square K , it will be BR : RK :: BA : AF . In either of these cafes , the distance required may be found by the rule of three * . Perpendicular ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 232 - E, is equal to twice as many right angles as the figure has sides, less four right angles.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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...
Seite 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...