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 52
... Elevation of the oblique Circle above the Plain of the Pro- jection . Q. E. D. But here it may be objected , That I use the Circle A e G both for the oblique Circle to be projected , and for its Repre- fentation in the Plain of the ...
... Elevation of the oblique Circle above the Plain of the Pro- jection . Q. E. D. But here it may be objected , That I use the Circle A e G both for the oblique Circle to be projected , and for its Repre- fentation in the Plain of the ...
Page 53
... Elevation fet from O , will find e a point thro ' which it must pass . PROP . V. If a leffer Circle whofe Poles lie in the plain of the Projection were to be pro- jected ; the Center of its Reprefenta- tion fhall be in the Line of ...
... Elevation fet from O , will find e a point thro ' which it must pass . PROP . V. If a leffer Circle whofe Poles lie in the plain of the Projection were to be pro- jected ; the Center of its Reprefenta- tion fhall be in the Line of ...
Page 64
... Elevation of the Pole , fo that the Poles Elevation in our Latitude being 51 ° . 30 ' , the Elevation of the Equinoctial above the Horizon will be 38 ° . 30 ' ; the Tangent of which being fet from z to n will give its Center , and the ...
... Elevation of the Pole , fo that the Poles Elevation in our Latitude being 51 ° . 30 ' , the Elevation of the Equinoctial above the Horizon will be 38 ° . 30 ' ; the Tangent of which being fet from z to n will give its Center , and the ...
Page 66
... Elevation above the Horizon : The Northern Part of the Ecliptick falls 23 ° 30 ' nearer the Zenith than the Equinoctial does , there- fore the Southern Part being brought a- bove the Horizon , must be 23 ° 30 ' near- er the Horizon than ...
... Elevation above the Horizon : The Northern Part of the Ecliptick falls 23 ° 30 ' nearer the Zenith than the Equinoctial does , there- fore the Southern Part being brought a- bove the Horizon , must be 23 ° 30 ' near- er the Horizon than ...
Page 72
... Elevation of this Cir- cle above the Horizon being the fame with that of the Pole , viz . $ 1 ° . 30 % ; take the Tangent of 51 ° . 30. and fet it from Z to K ; and upon the Center K , and with the Secant of the fame Elevati on describe ...
... Elevation of this Cir- cle above the Horizon being the fame with that of the Pole , viz . $ 1 ° . 30 % ; take the Tangent of 51 ° . 30. and fet it from Z to K ; and upon the Center K , and with the Secant of the fame Elevati on describe ...
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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.