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 2
... angles is a right angle , as ABC , fig . 2. & 3 .. 3. In a right - angled plane triangle ABC , fig . 1. the fide AB fubtending the right angle ACB , is called the hypo- thenufe ; and AC , CB , that contain the right angle , are called ...
... angles is a right angle , as ABC , fig . 2. & 3 .. 3. In a right - angled plane triangle ABC , fig . 1. the fide AB fubtending the right angle ACB , is called the hypo- thenufe ; and AC , CB , that contain the right angle , are called ...
Page 91
... angle ABC , radius , and the other fide AC . PROP . IV . THEOR . Fig . 12 . 4. Any two fides AB , BC , of any triangle ACB , are to one another as the fines of the angles BCA , BAC , oppofite to thefe fides ; that is , AB is to BC , as ...
... angle ABC , radius , and the other fide AC . PROP . IV . THEOR . Fig . 12 . 4. Any two fides AB , BC , of any triangle ACB , are to one another as the fines of the angles BCA , BAC , oppofite to thefe fides ; that is , AB is to BC , as ...
Page 92
... angle FAC , which , by construc- tion , is equal to the angle ACB , and BD is the fine of the arc BG , or of the angle BAC ; therefore AB is to BC , as the fine of the angle BCA to the fine of the angle BAC . Q.E. D. Cor . 1. Hence , if ...
... angle FAC , which , by construc- tion , is equal to the angle ACB , and BD is the fine of the arc BG , or of the angle BAC ; therefore AB is to BC , as the fine of the angle BCA to the fine of the angle BAC . Q.E. D. Cor . 1. Hence , if ...
Page 94
... angle , the fine of the angle oppofite to the given fide is to be made the first term of the proportionals . It is ... ACB , ABC , oppofite to thefe fides , to the tangent of half the dif- ference of the fame angles . Let AC be the greater ...
... angle , the fine of the angle oppofite to the given fide is to be made the first term of the proportionals . It is ... ACB , ABC , oppofite to thefe fides , to the tangent of half the dif- ference of the fame angles . Let AC be the greater ...
Page 95
... angle EAF is [ 32. 1. ] equal to half the fum of the angles ABC , ACB . Because EA is equal to AG , and the angle EAF to the angle GAF , EG [ 4. 1. ] is bifected at right angles by AF ; but EA is equal to AB , therefore AF and BG [ 2.6 ...
... angle EAF is [ 32. 1. ] equal to half the fum of the angles ABC , ACB . Because EA is equal to AG , and the angle EAF to the angle GAF , EG [ 4. 1. ] is bifected at right angles by AF ; but EA is equal to AB , therefore AF and BG [ 2.6 ...
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Elements of Trigonometry, Plane and Spherical: With the Principles of ... John Wright (mathematician ) No preview available - 2020 |
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.