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 |
From inside the book
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Page 23
... sine Bè : square rad . :: sine rad . x vers . sine suppt B -AC ; + AC ) x sine ( AB + BC + AC ) × sine ( AB + RC + AC ) or , sine AB × sine BC : rad . :: sine ( AB + BC vers . sine suppt B ( AB + BC + AC ) — AC : hence it follows that ร ...
... sine Bè : square rad . :: sine rad . x vers . sine suppt B -AC ; + AC ) x sine ( AB + BC + AC ) × sine ( AB + RC + AC ) or , sine AB × sine BC : rad . :: sine ( AB + BC vers . sine suppt B ( AB + BC + AC ) — AC : hence it follows that ร ...
Page 33
... sine of an arc is the versed sine of the complement of that arc . Thus , AE ... Rad A Car B A Sec A Rad CA ( X ) 3dly . If the perpendicular BC be ... Rad D INVESTIGATION OF RULES FOR CALCULATING THE SIDES AND ANGLES OF CHAP . I. 33 PLANE ...
... sine of an arc is the versed sine of the complement of that arc . Thus , AE ... Rad A Car B A Sec A Rad CA ( X ) 3dly . If the perpendicular BC be ... Rad D INVESTIGATION OF RULES FOR CALCULATING THE SIDES AND ANGLES OF CHAP . I. 33 PLANE ...
Page 40
... X BC Tiger , 2AB X BC AB2 + BC2 . AC2 :: rad . cos . / B. Q.E.D. NOTE . If the sides of the triangle be large , the ... sine of 90 ° . a CASE I. Given the angles and the hypothenuse , to find the base and perpendicular . sine A b • COS C ...
... X BC Tiger , 2AB X BC AB2 + BC2 . AC2 :: rad . cos . / B. Q.E.D. NOTE . If the sides of the triangle be large , the ... sine of 90 ° . a CASE I. Given the angles and the hypothenuse , to find the base and perpendicular . sine A b • COS C ...
Page 83
... ( rad . + sine CDB ) X DC DB 141.12 miles , and CE 7964 miles . Cosine CDB CHAP . IV . OBSERVATIONS ON THE ADMEASUREMENT OF A BASE LÍNE . ( G ) Where the ground is perfectly level , the manner of measuring a straight line from one object ...
... ( rad . + sine CDB ) X DC DB 141.12 miles , and CE 7964 miles . Cosine CDB CHAP . IV . OBSERVATIONS ON THE ADMEASUREMENT OF A BASE LÍNE . ( G ) Where the ground is perfectly level , the manner of measuring a straight line from one object ...
Page 85
... rad . : PD : sine DPB : DB , hence DB = PD X sine DPB rad . 119.93 toises . In order to cal- culate BS ; PD may be used instead of PB , and Cs and CB may be considered as equal to each other without sensible error . And as ( 2cs + BS ) X ...
... rad . : PD : sine DPB : DB , hence DB = PD X sine DPB rad . 119.93 toises . In order to cal- culate BS ; PD may be used instead of PB , and Cs and CB may be considered as equal to each other without sensible error . And as ( 2cs + BS ) X ...
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