A New & Complete Treatise of Spherical Trigonometry: In which are Contained the Orthographic, Analytical & Logarithmical Solutions of the Several Cases of Spherical Triangles ... a Comprehensive Theory of the Fluxions of These Triangles ...W. Adlard, 1768 - 216 sider |
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Vanlige uttrykk og setninger
AB-AC adjacent adjacent angles alfo analogy Ax fin bafe BD-CD becauſe cafes circle cofec confequently conftant conftruction COROLLARY correfponding cotangent deduced defcribed demonftrated difference eafily eafy ecliptic ellipfis equal equation expreffion faid fame fecant fecond fegments fhall fide AC figns fimilar triangles fimple fince fines firft fluxion folutions fome formula fphere fquare ftar fubftituting fuch fun's declination fupplement fuppofe furface given half the fum hypothenufe interfection laft latitude lefs let fall likewife logarithms manifeft meaſure multiple muſt neceffary Neper obferved obtufe oppofite fides perpendicular plane pole PROBLEM projection proportion radius right-angled triangles right-lined SCHOLIUM ſhall spherical triangle tang tangent tangent of half thefe Theorem theſe third fide thofe thoſe three angles three fides triangle BAC Trigonometry uſed whence whereof whofe x fin
Populære avsnitt
Side 83 - DE 5 or, that the tangtnt of half the bafe -is to the tangent of half the fum of the...
Side 83 - ... perpendicular to AD, meeting AB in E: shew that the triangles ABC, ACE are similar. 13. In any triangle, if a perpendicular be let fall upon the base from the vertical angle, the base will be to the sum of the sides, as the difference of the sides to the difference or sum of the segments of the base made by the perpendicular, according as it falls within or without the triangle. 14. If triangles AEF, ABC have a common angle A, triangle ABC:iIiwn^\eAEF::AB.AC:AE.AF.
Side 91 - As the cotangent of half the fum of the angles at the bafe, is to the tangent of half their difference, fo is the tangent of half the vertical angle, to the tangent of the angle which the perpendicular CD makes with the line CF, bifcding the vertical The Solution of the Cafes of righl-angled fpfierical Triangles, (Fig.
Side 27 - ... of any arc in parts of that arc, or in decimals of the radius ; that is, to calculate the «JMftz/ Jim and coßne of any arc*. * See " Expoßiion du Calcul Âflrtmomigue
Side 182 - ... the fame, the error of time will not be altered, whatever the altitude of the ftar in the given vertical be -t n г .л" , .' • '' *• Т О^ íince 7—15 will' be always à confiant quantity, 'jj •-"- • f •''>'•'••
Side 4 - And likewife inverfely and contrarily, which is plainly the fame thing ; becaufe the Radius is a mean proportional between the Tangent of an Arch, and...
Side 122 - BC, fo is the tangent of half the difference of tiefe fides to the tangent of half the difference of the fegments of the bafe.
Side 91 - ¡um cf the. angles at the bafe is to the fine of half their difference, as the tangent of half the fum of...
Side 87 - ... of half their difference, fo is the tangent of half the fide adjacent to thefe angles to the tangent of half the difference of their oppoftte fides j or, which is the fame. Si».
Side 55 - С is the pole of the arc EF, the points С and E will likewife be 90° diftant; therefore, by art.