A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical ApplicationsJ. Johnson, 1806 - 419 Seiten |
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Seite xxii
... if they are unlike . EXAMPLES . 1. In the right - angled spherical triangle , ABC , hav- ing the leg AC 54 ° 43 ′ , and its adjacent angle a 48 ° , to find the rest . AFFECTIONS OF RIGHT - ANGLED SPHERICAL TRIANGLES . 1. The 86.
... if they are unlike . EXAMPLES . 1. In the right - angled spherical triangle , ABC , hav- ing the leg AC 54 ° 43 ′ , and its adjacent angle a 48 ° , to find the rest . AFFECTIONS OF RIGHT - ANGLED SPHERICAL TRIANGLES . 1. The 86.
Seite xxviii
... EXAMPLES . 1. In the right - angled spherical triangle ABC , hav- ing the leg AC 54 ° 43 ′ , and the leg BC 42 ° 12 ′ , to find the rest . BY CONSTRUCTION . E m D a 1. From o , as a centre , with the chord of 60 ° de- scribe a circle ...
... EXAMPLES . 1. In the right - angled spherical triangle ABC , hav- ing the leg AC 54 ° 43 ′ , and the leg BC 42 ° 12 ′ , to find the rest . BY CONSTRUCTION . E m D a 1. From o , as a centre , with the chord of 60 ° de- scribe a circle ...
Seite 12
... EXAMPLE 1 . In the plane triangle ABC , AC 236 } Yards . Required the other parts . BC 350 LB 38 ° 40 ' B. ( h ) As the results in this rule are determined by means of the sines , which are always the same for an acute angle and its sup ...
... EXAMPLE 1 . In the plane triangle ABC , AC 236 } Yards . Required the other parts . BC 350 LB 38 ° 40 ' B. ( h ) As the results in this rule are determined by means of the sines , which are always the same for an acute angle and its sup ...
Seite 14
... EXAMPLE II . In the plane triangle ABC , = AB 131 Given BC 97 Lc 90 ° Ans . A C 88.045 ZA 47 ° 46 ′ 4 B 42 ° 14 ' Required the other parts . EXAMPLE III . In the plane triangle ABC , BC 14.
... EXAMPLE II . In the plane triangle ABC , = AB 131 Given BC 97 Lc 90 ° Ans . A C 88.045 ZA 47 ° 46 ′ 4 B 42 ° 14 ' Required the other parts . EXAMPLE III . In the plane triangle ABC , BC 14.
Seite 15
... EXAMPLE IV . In the plane triangle ABC , AB 195 Given AC 203 LB 45 ° ZA 92 ° 13 ' Ans . 4 c 42 ° 47 ' BC 286.87 Required the other parts . EXAMPLE V. In the plane triangle ABC , BC 345 AB 174.07 Given < AC 232 or 374.56 LB 37 ° 20 ' Ans ...
... EXAMPLE IV . In the plane triangle ABC , AB 195 Given AC 203 LB 45 ° ZA 92 ° 13 ' Ans . 4 c 42 ° 47 ' BC 286.87 Required the other parts . EXAMPLE V. In the plane triangle ABC , BC 345 AB 174.07 Given < AC 232 or 374.56 LB 37 ° 20 ' Ans ...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle Keine Leseprobe verfügbar - 2014 |
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
A B C acute adjacent angle Aldebaran ambiguous azimuth centre complement cos² cosec cosine describe a circle diff difference distance draw the diameters ecliptic equal equation Example extent will reach find the rest former formulæ given leg given side Given two sides greater than 90 Greenwich height horizon hypothenusal angle incd latitude leg BC less than 90 Log sine logarithms longitude meridian moon's oblique oblique-angled spherical triangle observed obtuse opposite angle parallax perpendicular plane triangle point of aries points pole quadrantal spherical triangle radius required to find right ascension right-angled spherical triangle RULE scale of chords secant semitangent side AC sides and angles sin a sin sin² sines sphere spherical angle spherical triangle ABC spherical trigonometry star subtracted sun's declination supplement tangents THEOREM three angles three sides trigonometry whence
Beliebte Passagen
Seite xxxi - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Seite 6 - ... for the second term, and the greater for the first ; and in either case multiply the second and third terms together, and divide the product by the first for the answer, which will always be of the same denomination as the third term.
Seite 329 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Seite 363 - The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side.
Seite vii - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Seite 13 - To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference...
Seite 17 - 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.
Seite 2 - SECANT of an arc, is a straight line drawn from the centre, through one end of the arc, and extended to the tangent which is drawn from the other end.
Seite 181 - The AMPLITUDE of any object in the heavens is an arc of the horizon, contained between the centre of the object when rising, or setting, and the east or west points of the horizon. Or, it is...
Seite 75 - Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them.