A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical ApplicationsJ. Johnson, 1806 - 419 Seiten |
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Seite xxix
... gives B 64 ° 35 ' , or , taken on the scale of semitangents , and then subtracted from 90 ° , gives 4 A 48 ° 0 ' , and AC , on the scale of chords , is 54 ° 43 ' . BY CALCULATION . : Sin AB : Rad , or sin :: Sin B C - · - - 64 ° 40 ' 90 ...
... gives B 64 ° 35 ' , or , taken on the scale of semitangents , and then subtracted from 90 ° , gives 4 A 48 ° 0 ' , and AC , on the scale of chords , is 54 ° 43 ' . BY CALCULATION . : Sin AB : Rad , or sin :: Sin B C - · - - 64 ° 40 ' 90 ...
Seite 11
... give the greater of those quantities ; and , if it be subtracted from the half sum , it will give the less . CASE I. When two of the three given things are a side and its opposite angle , to find the rest . RULE . The sides of any plane ...
... give the greater of those quantities ; and , if it be subtracted from the half sum , it will give the less . CASE I. When two of the three given things are a side and its opposite angle , to find the rest . RULE . The sides of any plane ...
Seite 16
... gives the greater angle , and subtracted from it gives the less . And as all the angles are now known , the remaining side may be found by Case I. Note . Instead of the tangent of half the sum of the two unknown angles , we may use the ...
... gives the greater angle , and subtracted from it gives the less . And as all the angles are now known , the remaining side may be found by Case I. Note . Instead of the tangent of half the sum of the two unknown angles , we may use the ...
Seite 19
... give the greater segment ; and , subtracted from it , will give the less . Then , in each of the right - angled triangles , formed by the perpendicular , there will be known two sides and an angle opposite to one of them ; from whence ...
... give the greater segment ; and , subtracted from it , will give the less . Then , in each of the right - angled triangles , formed by the perpendicular , there will be known two sides and an angle opposite to one of them ; from whence ...
Seite 31
... gives the opposite the greater of the two given sides ; and , subtracted from it , gives the Or , Tan ( BC ) = b + c opposite the less . cot A. L tan ÷ ( B −c ) = € 1 ( b + c ) + L ( b −c ) + L cot A — 10 . Then , ( 90 ° -A ) + ↓ ( B ...
... gives the opposite the greater of the two given sides ; and , subtracted from it , gives the Or , Tan ( BC ) = b + c opposite the less . cot A. L tan ÷ ( B −c ) = € 1 ( b + c ) + L ( b −c ) + L cot A — 10 . Then , ( 90 ° -A ) + ↓ ( B ...
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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.