A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical ApplicationsJ. Johnson, 1806 - 419 pages |
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Page xxviii
... centre , with the chord of 60 ° de- scribe a circle , and draw the diameter EC . 2. Set off CA ( 54 ° 43 ' ) from the scale of chords , and make or equal to the semitangent of the comple- ment of BC ( 47 ° 48 ′ ) . 3. Draw the diameters ...
... centre , with the chord of 60 ° de- scribe a circle , and draw the diameter EC . 2. Set off CA ( 54 ° 43 ' ) from the scale of chords , and make or equal to the semitangent of the comple- ment of BC ( 47 ° 48 ′ ) . 3. Draw the diameters ...
Page 3
... centre of the circle and the sine . Thus B F , or its equal o D , is the cosine of A B or of Ba , or the sine of its complement в с . a C F B A D The tangent of an arc , is a right line drawn perpen- dicular to the diameter , at one end ...
... centre of the circle and the sine . Thus B F , or its equal o D , is the cosine of A B or of Ba , or the sine of its complement в с . a C F B A D The tangent of an arc , is a right line drawn perpen- dicular to the diameter , at one end ...
Page 4
... centre , through one end of the arc , and terminated by the tangent , or a line drawn perpendicular to the diameter at the other end . Thus OE is the secant of A B , or of в а . B E a A e The cosecant of an arc is the secant of the ...
... centre , through one end of the arc , and terminated by the tangent , or a line drawn perpendicular to the diameter at the other end . Thus OE is the secant of A B , or of в а . B E a A e The cosecant of an arc is the secant of the ...
Page 13
... centre c , and radius 236 , taken from the same scale of equal parts , cross BA in a or a . 4. Join ca or ca , and the triangle ABC , or aвс , is the one required . Then , the Zs c and A , measured by the scale of chords , and the side ...
... centre c , and radius 236 , taken from the same scale of equal parts , cross BA in a or a . 4. Join ca or ca , and the triangle ABC , or aвс , is the one required . Then , the Zs c and A , measured by the scale of chords , and the side ...
Page 19
... centres b , c , and radii 464 and 348 , taken from the same scale , describe arcs intersecting each other in A. 3. Join AB , AC , and the triangle is constructed .. Then , by measuring the angles with a protractor , or by the scale of ...
... centres b , c , and radii 464 and 348 , taken from the same scale , describe arcs intersecting each other in A. 3. Join AB , AC , and the triangle is constructed .. Then , by measuring the angles with a protractor , or by the scale of ...
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.