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 10
... likewise evident , that any Ark as CC is projected into OO , equal to Ca , Cb or Cd , which is the right Sine of that Ark ; and the complemental Ark CA is projected into OA , the Verfed Sine of the fame Ark CC . COR . III . Hence it is ...
... likewise evident , that any Ark as CC is projected into OO , equal to Ca , Cb or Cd , which is the right Sine of that Ark ; and the complemental Ark CA is projected into OA , the Verfed Sine of the fame Ark CC . COR . III . Hence it is ...
Page 12
... because BF is at right Angles to the Plain of the Projection , the plain ABF will also be at right Angles to it ; and since DA is perpendicular to BA , it will likewise likewife be perpendicular to FA , año- ther Line in ( 12 )
... because BF is at right Angles to the Plain of the Projection , the plain ABF will also be at right Angles to it ; and since DA is perpendicular to BA , it will likewise likewife be perpendicular to FA , año- ther Line in ( 12 )
Page 41
... likewise op- posed to the Eye at A ; Wherefore the two Plains BDCE and KGIF will be parallel to one another , and confequent- ly the Cone of Rays AKGIF will be cut by the Plain of the Projection in kgif , which being in the Plain of the ...
... likewise op- posed to the Eye at A ; Wherefore the two Plains BDCE and KGIF will be parallel to one another , and confequent- ly the Cone of Rays AKGIF will be cut by the Plain of the Projection in kgif , which being in the Plain of the ...
Page 67
... likewise be at right Angles to all lesser Circles parallel to the Equinoctial ; and the fame will hold with regard to Circles parallel to the Ecliptick : But NS is the Line of Measures of the Equinoctial and Ecliptick , and confequently ...
... likewise be at right Angles to all lesser Circles parallel to the Equinoctial ; and the fame will hold with regard to Circles parallel to the Ecliptick : But NS is the Line of Measures of the Equinoctial and Ecliptick , and confequently ...
Page 77
... paffes thro ' the North and South Points , will likewise be per- pendicular to the Ecliptick ; wherefore its Line of Measures will be N S , and its Center may be found by fetting the Tangent of its ( 77 ) E the Eaft, S the South, and W ...
... paffes thro ' the North and South Points , will likewise be per- pendicular to the Ecliptick ; wherefore its Line of Measures will be N S , and its Center may be found by fetting the Tangent of its ( 77 ) E the Eaft, S the South, and W ...
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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.