A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical ApplicationsJ. Johnson, 1806 - 419 pages |
From inside the book
Results 1-5 of 60
Page x
... formulæ for the chords , and consequently sines , of the sums and dif- ferences of arcs , and such as are in arithmetical pro- gression ; which have since been so extensively and ( e ) This curious performance , which was published ...
... formulæ for the chords , and consequently sines , of the sums and dif- ferences of arcs , and such as are in arithmetical pro- gression ; which have since been so extensively and ( e ) This curious performance , which was published ...
Page xxi
... formulæ by Delambre ; and the tables lately published at Berlin , by Hobert and Ideler , which are also adapted to the decimal division of the circle , and are highly praised for their accuracy by the French computors . Among the ...
... formulæ by Delambre ; and the tables lately published at Berlin , by Hobert and Ideler , which are also adapted to the decimal division of the circle , and are highly praised for their accuracy by the French computors . Among the ...
Page xxii
... formulæ in the table of cases , page 146 et seq . , where the limits of the data , and other circumstances , are more particularly pointed out . CASE II . When a leg and its adjacent angle are given , to find the rest . 1. To find the ...
... formulæ in the table of cases , page 146 et seq . , where the limits of the data , and other circumstances , are more particularly pointed out . CASE II . When a leg and its adjacent angle are given , to find the rest . 1. To find the ...
Page xxiv
... formulæ which have since enriched this branch of the subject . We are also , in this respect , no less indebted to Na- pier , not only for his admirable discovery of logarithms , but for the new and excellent analogies which he in ...
... formulæ which have since enriched this branch of the subject . We are also , in this respect , no less indebted to Na- pier , not only for his admirable discovery of logarithms , but for the new and excellent analogies which he in ...
Page xxv
... formulæ ; and by this means assimilated the principles of loga- rithms and trigonometry with those of the new calculi , of which they were the inventors and improvers . 1 The exponential formulæ , also , for the sines and XXV.
... formulæ ; and by this means assimilated the principles of loga- rithms and trigonometry with those of the new calculi , of which they were the inventors and improvers . 1 The exponential formulæ , also , for the sines and XXV.
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.