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 10
... equal angles , pro- portionals ; wherefore GC is to CH , as GD to DL : but the three firft terms of the ... equal to the cofine of GHB , is alfo the fine of forty - five degrees , and is therefore equal to GP ; and because the fquare of ...
... equal angles , pro- portionals ; wherefore GC is to CH , as GD to DL : but the three firft terms of the ... equal to the cofine of GHB , is alfo the fine of forty - five degrees , and is therefore equal to GP ; and because the fquare of ...
Page 11
... equal to the two angles CDB , CBD , and [ 5. 1. ] double of one of them CDB ; therefore the angle CDB is double of the angle DCB ; and because DE is [ cor . 15. 4. equal to DC , the angle DCE is [ 5. 1. ] equal to the angle DEC , and ...
... equal to the two angles CDB , CBD , and [ 5. 1. ] double of one of them CDB ; therefore the angle CDB is double of the angle DCB ; and because DE is [ cor . 15. 4. equal to DC , the angle DCE is [ 5. 1. ] equal to the angle DEC , and ...
Page 12
... equal to the angle CDB ; and [ 4. 6. ] BE is to BC , as BC to BD : but [ cor . 15. 4. ] -BC is equal to ED ; therefore BE is to ED , as ED to DB . Q. E. D. PROP . VII . THEOR . Fig : 7 . Which is the ioth of the 13th book of Euclid . 22 ...
... equal to the angle CDB ; and [ 4. 6. ] BE is to BC , as BC to BD : but [ cor . 15. 4. ] -BC is equal to ED ; therefore BE is to ED , as ED to DB . Q. E. D. PROP . VII . THEOR . Fig : 7 . Which is the ioth of the 13th book of Euclid . 22 ...
Page 13
... equal to the circumference CG . And because FL is at right angles to AH , the angle AFK is [ 3. 3. & 8. 1. ] equal to the angle KFH , and the circumference AK [ 26. 3. ] to the circumference KH ; wherefore the circumference GCB is dou ...
... equal to the circumference CG . And because FL is at right angles to AH , the angle AFK is [ 3. 3. & 8. 1. ] equal to the angle KFH , and the circumference AK [ 26. 3. ] to the circumference KH ; wherefore the circumference GCB is dou ...
Page 14
... equal to the fquare of AH : but the fquare of BF was shown to be equal to the rect- angle ABM ; therefore the fquares of BF and AH are equal to the rectangles ABM and BAM ; that is , [ 2. 2. ] to the square of AB . QE . D. PROP . VIII ...
... equal to the fquare of AH : but the fquare of BF was shown to be equal to the rect- angle ABM ; therefore the fquares of BF and AH are equal to the rectangles ABM and BAM ; that is , [ 2. 2. ] to the square of AB . QE . D. PROP . VIII ...
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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.