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 - 251 Seiten |
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Seite 19
... contained by radius , and half the fum of the fines of two unequal arcs GH and GHL , is equal to the rect- angle ... rectangle 1 rectangle contained by CK and OP is equal to Sect . I. 19 TRIGONOMETRY .
... contained by radius , and half the fum of the fines of two unequal arcs GH and GHL , is equal to the rect- angle ... rectangle 1 rectangle contained by CK and OP is equal to Sect . I. 19 TRIGONOMETRY .
Seite 20
... rectangle contained by CK and OP is equal to the rectangle contained by KE and CO . Q. E. D. Cor . Hence , if KE , the fine of half the fum of two arcs GH , GHL , and CO , the cofine of half their difference , be each of them given , OP ...
... rectangle contained by CK and OP is equal to the rectangle contained by KE and CO . Q. E. D. Cor . Hence , if KE , the fine of half the fum of two arcs GH , GHL , and CO , the cofine of half their difference , be each of them given , OP ...
Seite 54
... rectangle contained by the difference of any two terms , taken on the afymptote , and by the difference of the two correfponding terms of the ordinates , is equal to the rectangle contained by the difference of any other two terms taken ...
... rectangle contained by the difference of any two terms , taken on the afymptote , and by the difference of the two correfponding terms of the ordinates , is equal to the rectangle contained by the difference of any other two terms taken ...
Seite 56
... rectangle AGK is alfo I ; and be- cause AG is 2 , GK or EP is ; wherefore EGKP is [ 1. 6. ] one half of AD . ( 2 ) ... contained by HQ , and by QP } ; and is therefore of AD . TZ ( 3 ) Bifect FE in L , and draw LM , MR , as before ; and ...
... rectangle AGK is alfo I ; and be- cause AG is 2 , GK or EP is ; wherefore EGKP is [ 1. 6. ] one half of AD . ( 2 ) ... contained by HQ , and by QP } ; and is therefore of AD . TZ ( 3 ) Bifect FE in L , and draw LM , MR , as before ; and ...
Seite 57
... rectangle MQ . ( 4 ) Bifect FG in N , and complete the rectangle FO ... found to be , T1 , T2 , I 2401 14 I I I 40 , of AD ; and this feries ... contain an angle of 54 ° 16 ' . Mercator likewife difcovered an infinite feries , expreffing ...
... rectangle MQ . ( 4 ) Bifect FG in N , and complete the rectangle FO ... found to be , T1 , T2 , I 2401 14 I I I 40 , of AD ; and this feries ... contain an angle of 54 ° 16 ' . Mercator likewife difcovered an infinite feries , expreffing ...
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Elements of Trigonometry, Plane and Spherical: With the Principles of ... John Wright (mathematician ) Keine Leseprobe verfügbar - 2020 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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...
Seite 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.
Seite 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.
Seite 94 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Seite 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.
Seite 164 - If a solid angle be contained by three plane angles, any two of them are together greater than the third.
Seite 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...
Seite 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...
Seite 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.
Seite 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.