Elements of Plain and Spherical Trigonometry: Together with the Principles of Spherick Geometry, and the Several Projections of the Sphere in Plano. The Whole Demonstrated and Illustrated with Useful Cases and Examples |
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Page 16
... fince P , a length is fought , that must be the laft of the Four Terms ; place it therefore laft with an Interrogation- point after it , to fhew that it is re required or fought . In the Golden Rule the second and fourth Terms being ...
... fince P , a length is fought , that must be the laft of the Four Terms ; place it therefore laft with an Interrogation- point after it , to fhew that it is re required or fought . In the Golden Rule the second and fourth Terms being ...
Page 18
... fince B a length is given of the fame Nature with H , that must be in the second place : And then fay by Axiom 1. As B confidered as the Sine of the given Angle a , is to its felf confidered as a length ; fo is H confidered as Radi- us ...
... fince B a length is given of the fame Nature with H , that must be in the second place : And then fay by Axiom 1. As B confidered as the Sine of the given Angle a , is to its felf confidered as a length ; fo is H confidered as Radi- us ...
Page 37
... fince the Triangle c a dis Right- angled , ( by what is proved below in the next Figure fave one ) if ad be made Radius , cd will be the Tangent of the Angle cad ( i . e . the Tangent of Sum of oppofite Angles ; ) and in the little ...
... fince the Triangle c a dis Right- angled , ( by what is proved below in the next Figure fave one ) if ad be made Radius , cd will be the Tangent of the Angle cad ( i . e . the Tangent of Sum of oppofite Angles ; ) and in the little ...
Page 52
... , and b will be the Course . Prick off the Distance run , viz . 51.5 Miles from 6 to a . Then because the Ship failed W. S. W. the contrary Rumb from a to b , must be E.N.E : ENE : And fince the South Eaft Rumb makes with ( 52 )
... , and b will be the Course . Prick off the Distance run , viz . 51.5 Miles from 6 to a . Then because the Ship failed W. S. W. the contrary Rumb from a to b , must be E.N.E : ENE : And fince the South Eaft Rumb makes with ( 52 )
Page 53
... fince the South Eaft Rumb makes with that , an Angle of 67 ° 30 ' , you must make the Angle at 4 , juft 67 ° 30 ' . So will the Line H , when drawn , interfect the Line B in the Point of the Situation of the Head Land ; and by that ...
... fince the South Eaft Rumb makes with that , an Angle of 67 ° 30 ' , you must make the Angle at 4 , juft 67 ° 30 ' . So will the Line H , when drawn , interfect the Line B in the Point of the Situation of the Head Land ; and by that ...
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Elements of Plain and Spherical Trigonometry: Together with the Principles ... John Harris No preview available - 2017 |
Common terms and phrases
alfo alſo Angular Point Axiom Bafe Baſe becauſe Cafe Center Chords Circle paffing Co-fine Complement confequently Courſe cuts the Plain defcribe the Circle Diſtance draw the Diameter draw the Line eaſily Eaſt Ecliptick Elevation Equinoctial fall fame manner fhall fimilar fince firft firſt folved fome fuch fuppofe fures greateſt half Tangent Horizon Hour-Circles Hypothenufe Interfection laft Latitude leffer Circle lefs Legs Lemma likewife Line of Meaſures Logarithm muſt neareſt number of Degrees oblique Circle oppofite Angles Orthographick paffing thro Parallels of Declination paſs pendicular perpendicular Polar Circles Pole prefent primitive Circle PROB Projection Quadrant Radius rallel reprefent repreſent Repreſentation right Angles right Circle right Line Right-angled Triangles Secant Sides Sphere Spherical Angle Spherick ther theſe thofe thoſe Trigonometry Tropick uſe Verfed Sine Weft wherefore whofe Zenith
Popular passages
Page 160 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...
Page 41 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Page 159 - BD ; the co-fine of the angle B will be to the co-fine of the angle D, as the fine of the angle BCA to the fine of the angle DCA. For by 22. the co-fine of the angle B is to the fine of the angle...
Page 11 - If either of the legs, including the right angle, be made the radius of a circle, the other leg will be the tangent of its oppofite angle, and the hypothenufe the fecant of the fame angle, E For TRIGONOMETRY.
Page 35 - In any plane triangle, the sum of tfte two sides containing either angle, is to their difference, as the tangent of half the sum of the other two angles, to the tangent of half their difference.
Page 40 - Sum of fs'' \ the Legs, as the Difference of the Legs is to the Difference of the Segments of the Bafe made by a Perpendicular let fall from the Angle oppofite to the Bafe.
Page 166 - Angle oppoflte call the Bafe ; then work as in the nth Cafe. For fuch is the Operation in the Supplemental Triangle, whofe Angles and Sides are equal to the Supplements of the Sides and Angles of the Triangle propnk'd ; and Arcs and their Supplements have the fame Sines and Tangents.
Page 56 - Projeftiott the Angles made by the Circles on the Surface of the Sphere are equal to the Angles made by their Reprefentatiyes on the plane of the Projection.
Page 38 - FA : FG ; that is in Words, half the Sum of the Legs is to half their Difference, as the Tangent of half the Sum of the oppofite Angles is to the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum of the Legs...
Page 158 - OBlique Spherical Triangles may be reduced to two Right-angled Spherical Triangles, by letting fall a Perpendicular, which Perpendicular eiPlate V.