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 17
... Sphere upon this Circle for Lat . 51 ° . 30 ' . and fhew fome of those many Uses that may be made of this Pro- jection , which is ufually called the Ana- temma . C PROB . PROB . II . To Project the Equinoctial Colure , ( 17 )
... Sphere upon this Circle for Lat . 51 ° . 30 ' . and fhew fome of those many Uses that may be made of this Pro- jection , which is ufually called the Ana- temma . C PROB . PROB . II . To Project the Equinoctial Colure , ( 17 )
Page 18
... Equinoctial Colure , the Horizon for any Latitude , the E- quator , Tropicks , Polar Circles , E- cliptick , Parallels of Latitude , Pa- rallels of Declination , and Almacan- ters or Parallels of Altitude . Since all these Circles are ...
... Equinoctial Colure , the Horizon for any Latitude , the E- quator , Tropicks , Polar Circles , E- cliptick , Parallels of Latitude , Pa- rallels of Declination , and Almacan- ters or Parallels of Altitude . Since all these Circles are ...
Page 24
... Equinoctial , and from the Ecliptick , ( i . e . ) its Declination and Latitude ; fuppofe the Declination of a Star be 17 ° . N. and its Lat . 30 ° . N. and it were required to project this Star Orthographically : Firft fet the Chord of ...
... Equinoctial , and from the Ecliptick , ( i . e . ) its Declination and Latitude ; fuppofe the Declination of a Star be 17 ° . N. and its Lat . 30 ° . N. and it were required to project this Star Orthographically : Firft fet the Chord of ...
Page 25
... Equinoctial point , which is Libra , and you'll find it to be 45 ° . which taken from the Sines , and fet from the Center in the Ecliptick , will give the point , viz . the Suns place in the Ecliptick at that time , then through O ...
... Equinoctial point , which is Libra , and you'll find it to be 45 ° . which taken from the Sines , and fet from the Center in the Ecliptick , will give the point , viz . the Suns place in the Ecliptick at that time , then through O ...
Page 63
... Equinoctial , and here we must first determin the Line of Measures in which the Center of this Circle will be ; and this will be done by determining in what points a plain perpendicular to the Pri mitive and Equinoctial will cut the Ho ...
... Equinoctial , and here we must first determin the Line of Measures in which the Center of this Circle will be ; and this will be done by determining in what points a plain perpendicular to the Pri mitive and Equinoctial will cut the Ho ...
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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.