An Introduction to the Theory and Practice of Plane and Spherical Trigonometry, and the Stereographic Projection of the Sphere: Including the Theory of NavigationLongman, Hurst, Rees, Orme, and Brown, 1820 - 442 pages |
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Page 88
... arc PS . Now ( ASP + BPS ) - ( Asa + BPb ) ( OSP + OPS ) - ( Asa + BPb ) LC ... mean refraction . ( Z ) If one of the objects ( A ) instead of being ... arc PS ) by the Z of elevation e SA . Hence / c + Le SA LMSP + Lmps , from each of ...
... arc PS . Now ( ASP + BPS ) - ( Asa + BPb ) ( OSP + OPS ) - ( Asa + BPb ) LC ... mean refraction . ( Z ) If one of the objects ( A ) instead of being ... arc PS ) by the Z of elevation e SA . Hence / c + Le SA LMSP + Lmps , from each of ...
Page 96
... mean pa- rallax is only 8 " .6 . The moon's greatest horizontal parallax is 61'.32 " . least 54.4 " . ( T ) The ... arc is equal to the sine of its supplement , therefore sine GAC sine GAK , and GAK is the complement of GAE , therefore sine ...
... mean pa- rallax is only 8 " .6 . The moon's greatest horizontal parallax is 61'.32 " . least 54.4 " . ( T ) The ... arc is equal to the sine of its supplement , therefore sine GAC sine GAK , and GAK is the complement of GAE , therefore sine ...
Page 102
... arc . The angle brв being in a semicircle , is a right angle ( Euclid 31 of III . ) And FG , by the definition of a ... mean proportional be- tween the versed sine of that arc , and the versed sine of its sup- plement . For the Q. E. D. ...
... arc . The angle brв being in a semicircle , is a right angle ( Euclid 31 of III . ) And FG , by the definition of a ... mean proportional be- tween the versed sine of that arc , and the versed sine of its sup- plement . For the Q. E. D. ...
Page 118
... arcs EO and BA , and therefore BE is half the sum of the arcs Bо and BA ( C. 35. ) But BO + BA BO + ( BO + OE + AE ) = BO + ( BO + 20E ) = 2Bo + 20E2BE , that is the sum of the extreme arcs , BO and BA , is equal to double the mean arc ...
... arcs EO and BA , and therefore BE is half the sum of the arcs Bо and BA ( C. 35. ) But BO + BA BO + ( BO + OE + AE ) = BO + ( BO + 20E ) = 2Bo + 20E2BE , that is the sum of the extreme arcs , BO and BA , is equal to double the mean arc ...
Page 119
... mean arc :: double the sine of the mean arc : versed sine of double the mean arc . CB : BR :: ZX ( = 2rc ) : zv : 6 radius sine of the mean arc :: double the cosine of the mean arc : sine of twice the mean arc . CB : BR :: AO ( = 2on ) ...
... mean arc :: double the sine of the mean arc : versed sine of double the mean arc . CB : BR :: ZX ( = 2rc ) : zv : 6 radius sine of the mean arc :: double the cosine of the mean arc : sine of twice the mean arc . CB : BR :: AO ( = 2on ) ...
Other editions - View all
An Introduction to the Theory and Practice of Plain and Spherical ... Thomas Keith No preview available - 2017 |
An Introduction to the Theory and Practice of Plain and Spherical ... Thomas Keith No preview available - 2014 |
Common terms and phrases
acute altitude Answer apparent altitude azimuth base centre circle co-tangent complement construction cosec cosine degrees diff difference of latitude difference of longitude draw ecliptic equator Euclid find the angle formulæ given side greater Greenwich half the sum Hence horizon horizontal parallax hypoth hypothenuse less log sine mean arc measured meridian miles moon's N.sine N.cos natural number Naut Nautical Almanac noon North oblique observed obtuse parallax perpendicular plane triangle Plate pole PROPOSITION quadrant rad rad rad sine Rad x sine rad2 radius rhumb line right angles right ascension right-angled spherical triangle RULE sailed SCHOLIUM secant shewn side AC sine A sine sine BC sphere spherical angle spherical triangle ABC spherical trigonometry star star's straight line subtract sun's declination supplement tang tangent tangent of half three angles three sides Trigonometry true versed sine