Elements of Trigonometry, Plane and Spherical: With the Principles of Perspective, and Projection of the Sphere. By John WrightA. Murray & J. Cochran. Sold by A. Kincaid & W. Creech, W. Gray, and J. Bell; by D. Baxter, Glasgow, 1772 - Perspective - 251 pages |
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Page viii
... unit , and to be divided in- to decimal parts . The radius of Regiomon- tanus therefore is 10000000. The fame e- minent person also added to trigonometry the use of tangents , and calculated tables in parts of the radius for every ...
... unit , and to be divided in- to decimal parts . The radius of Regiomon- tanus therefore is 10000000. The fame e- minent person also added to trigonometry the use of tangents , and calculated tables in parts of the radius for every ...
Page 6
... fecants . HE radius of the circle is con- 5. THE fidered as unit , and is fuppo- fed to be divided into 1000ooco or more decimal parts . The fine , tangent , and fecant , fecant , of each degree and minute of the quadrant 6 Int . PLANE.
... fecants . HE radius of the circle is con- 5. THE fidered as unit , and is fuppo- fed to be divided into 1000ooco or more decimal parts . The fine , tangent , and fecant , fecant , of each degree and minute of the quadrant 6 Int . PLANE.
Page 29
... unit . Thus , 6 in the arithme- tical series shews that the corresponding term 64 , in the geometrical feries , is in the fixth place from unit . 8. If any number of terms of the arith- metical metical series be added together , the fum ...
... unit . Thus , 6 in the arithme- tical series shews that the corresponding term 64 , in the geometrical feries , is in the fixth place from unit . 8. If any number of terms of the arith- metical metical series be added together , the fum ...
Page 30
... unit , its fquare , its cube , its fourth power , & c . make a feries in geometrical proportion ; as , 2 , 4 , 8 , 16 , in the prefent example ; twice the logarithm of the number is the loga- rithm of its fquare ; three times the loga ...
... unit , its fquare , its cube , its fourth power , & c . make a feries in geometrical proportion ; as , 2 , 4 , 8 , 16 , in the prefent example ; twice the logarithm of the number is the loga- rithm of its fquare ; three times the loga ...
Page 32
... unit . The firft of thefe imperfections is remedied by dividing each term into a great number of decimal places ; and the lait , by intert- ing fo many terms , as that their difference may not much exceed unit . 16. A geometrical 1 , 10 ...
... unit . The firft of thefe imperfections is remedied by dividing each term into a great number of decimal places ; and the lait , by intert- ing fo many terms , as that their difference may not much exceed unit . 16. A geometrical 1 , 10 ...
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Common terms and phrases
ABCD adjacent alfo angle ABC angle ACB angle BAC angle BCA angle contained arithmetical mean bafe baſe becauſe centre circumference cofine cofine of BA complement conftructed contained by radius defcribed diameter divifions Extend the compaffes fame fecant fecond fect feries fhadow fhall reach fide AC firſt fourth proportional fquare ftraight lines fubtract geometrical mean geometrical plane given Hence hypothenufe join leffer circle likewife line of numbers lines of fines lines of tangents loga marked tan meaſure meeting number of degrees oblique-angled oppofite parallel diſtance perfpective plane perpendicular perſpective plane triangles pole PROP proper fraction propofition Q. E. D. Cor quadrant rectangle contained right angles right-angled ſpherical triangle rithm ſcale ſector ſhall ſpace ſphere ſpherical angle ſquare tangent of half terreftrial line thefe THEOR theſe three terms triangle ABC trigonometry wherefore whofe whoſe
Popular passages
Page 81 - Proportion by the line of lines. Make the lateral distance of the second term the parallel distance of the first term ; the parallel distance of the third term is the fourth proportional. Example. To find a fourth proportional to 8, 4, and 6, take the lateral distance of 4, and make it the parallel distance of 8 ; then the parallel distance of 6, extended from the centre, shall reach to the fourth proportional 3, In the same manner a third proportional is found to two numbers. Thus, to find a third...
Page 2 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Page 82 - Thus, if it were required to find a fourth proportional to 4, 8, and 6; because the lateral distance of the second term 8 cannot be made the parallel distance of the first term 4, take the lateral distance of 4, viz. the half of 8, and make it the parallel distance of the first term 4 ; then the parallel distance of the third term 6, shall reach from the centre to 6, viz.
Page 94 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Page 82 - ... reach to the fourth proportional 3. In the same manner, a third proportional is found to two numbers. Thus, to find a third proportional to 8 and 4, the sector remaining as in the former example, the parallel distance of 4, extended from the centre, shall reach to the third proportional 2.
Page 164 - If a solid angle be contained by three plane angles, any two of them are together greater than the third.
Page 27 - N. and if the firft be a multiple, or part of the fecond ; the third is the fame multiple, or the fame part of the fourth. Let A be to B, as C is to D ; and firft let A be a multiple of B ; C is the fame multiple of D. Take E equal to A, and whatever multiple A or E is of B, make F the fame multiple of D. then becaufe A is to B, as C is to D ; and of B the fecond and D the fourth equimultiples have been taken E and F...
Page 74 - From 1 to 2 From 2 to 3 From 3 to 4 From 4 to 5 From 5 to 6 From 6 to 7 From 7 to 8 From 8 to 9...
Page 39 - But in logarithms, division is performed by subtraction ; that is, the difference of -the logarithms of two num-bers, is the logarithm of the quotient of those numbers.
Page 237 - ... circumpolar, or so near to the elevated pole as to perform its apparent daily revolution about it without passing below the horizon, then the latitude of the place will be equal to the sum of the true altitude, and the codeclination or polar distance of the object; for this sum will obviously measure the elevation of the pole above the horizon, which is equal to the latitude.