A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical ApplicationsJ. Johnson, 1806 - 419 pages |
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Page xxviii
... semitangent of the comple- ment of BC ( 47 ° 48 ′ ) . 3. Draw the diameters Aa , Dd , at right angles to each other , and through the points A , B , a , describe a circle ; then ABC will be the triangle required . 3. Then pn , on the ...
... semitangent of the comple- ment of BC ( 47 ° 48 ′ ) . 3. Draw the diameters Aa , Dd , at right angles to each other , and through the points A , B , a , describe a circle ; then ABC will be the triangle required . 3. Then pn , on the ...
Page xxix
... semitangents , and then subtracted from 90 ° , gives ∠ A 48 ° 0 ' , and ac , on the scale of chords , is 54 ° 43 ′ . BY CALCULATION . .. - - - : Sin AB : Rad , or sin :: Sin в с : Sin ∠ A - - - - .. - .. 64 ° 40 ′ 90 ° .. - - - 42 ...
... semitangents , and then subtracted from 90 ° , gives ∠ A 48 ° 0 ' , and ac , on the scale of chords , is 54 ° 43 ′ . BY CALCULATION . .. - - - : Sin AB : Rad , or sin :: Sin в с : Sin ∠ A - - - - .. - .. 64 ° 40 ′ 90 ° .. - - - 42 ...
Page 83
... semitangent of the complement of the angle A ( 42 ° 0 ' ) from o tom , and through the three points a , m , a , describe a circle . 3. From o as a centre , with the semitangent of the complement of вс ( 47 ° 48 ′ ) as a radius ...
... semitangent of the complement of the angle A ( 42 ° 0 ' ) from o tom , and through the three points a , m , a , describe a circle . 3. From o as a centre , with the semitangent of the complement of вс ( 47 ° 48 ′ ) as a radius ...
Page 84
... semitangent of the given ∠ A ( 48 ° 0 ′ ) from o top ; and take c p equal to the chord of 90 ° . 2. Through the points B , p , draw the line пper , cutting the circle in n and r . 3. Then pn , taken on the scale of chords , gives the ...
... semitangent of the given ∠ A ( 48 ° 0 ′ ) from o top ; and take c p equal to the chord of 90 ° . 2. Through the points B , p , draw the line пper , cutting the circle in n and r . 3. Then pn , taken on the scale of chords , gives the ...
Page 87
... semitangent of the complement of the angle A ( 42 ° ) from o to m ; and through the points A , m , a , describe a circle . 3. Set off AC ( 54 ° 43 ' ) by the scale of chords , and draw co , cutting the circle ama in B ; then ABC will be ...
... semitangent of the complement of the angle A ( 42 ° ) from o to m ; and through the points A , m , a , describe a circle . 3. Set off AC ( 54 ° 43 ' ) by the scale of chords , and draw co , cutting the circle ama in B ; then ABC will be ...
Other editions - View all
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle No preview available - 2014 |
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle No preview available - 2018 |
Common terms and phrases
acute adjacent angle Aldebaran ambiguous azimuth centre complement cosec cosine describe a circle diff difference distance draw the diameters ecliptic equal equation Example extent will reach find the hypothenuse find the rest former formulæ given leg given side greater than 90 Greenwich height horizon hyp¹ hypothenusal angle incd latitude leg AC less than 90 Log sine logarithms longitude meridian moon's oblique oblique-angled spherical triangle observed obtuse opposite angle parallax perpendicular plane triangle points pole quadrantal spherical triangle radius rcos required to find right ascension right-angled spherical triangle RULE scale of chords secant semitangent side AC side is less sides and angles sin a sin sines sphere spherical angle spherical triangle A B C spherical trigonometry star subtracted sun's declination supplement tangents THEOREM three angles three sides triangle ABC trigonometry whence Μπ вс
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 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.
Page 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...
Page 75 - Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them.