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 |
From inside the book
Results 1-5 of 36
Page 3
... straight lines meeting in one point E , are , toge- ther , equal to four right angles , the whole circumference of a ... line HR , placed in a circle BCAD , fig . 4. is the chord of each of the circumferences or arcs HBR , HAR , cut off by ...
... straight lines meeting in one point E , are , toge- ther , equal to four right angles , the whole circumference of a ... line HR , placed in a circle BCAD , fig . 4. is the chord of each of the circumferences or arcs HBR , HAR , cut off by ...
Page 8
... straight line DF , are each of them gi- ven . For example , if the arc DB be thirty degrees , its fine is [ 1. of this ] 5000000 of the parts whereof radius is 10000000. If therefore the fquare of 5000000 be fubtracted from the square ...
... straight line DF , are each of them gi- ven . For example , if the arc DB be thirty degrees , its fine is [ 1. of this ] 5000000 of the parts whereof radius is 10000000. If therefore the fquare of 5000000 be fubtracted from the square ...
Page 9
... straight line DB , are each of them given . But the half of the chord DB is [ def . 2. of this ] the fine of half the arc DB . Which was to be done . Thus , if the arc DB be thirty degrees , its fine DH being [ 1. of this ] 5000000 ...
... straight line DB , are each of them given . But the half of the chord DB is [ def . 2. of this ] the fine of half the arc DB . Which was to be done . Thus , if the arc DB be thirty degrees , its fine DH being [ 1. of this ] 5000000 ...
Page 16
... straight line EB or EC is given ; and because the straight line EC , and a part of it DE , are each of them given , the remainder DC is given ; wherefore the fum of the fquares of DC and DB , that is , [ 47. 1. ] the fquare of CB , and ...
... straight line EB or EC is given ; and because the straight line EC , and a part of it DE , are each of them given , the remainder DC is given ; wherefore the fum of the fquares of DC and DB , that is , [ 47. 1. ] the fquare of CB , and ...
Page 17
... straight line AE is given ; but the half of the straight line AE is [ def . 2. of this ] the fine of half of the arc EA . Which was to be found . PROP . XI . PROB . Fig . 10 . 26. AB and EF , the fines of the given arcs KB and KF ...
... straight line AE is given ; but the half of the straight line AE is [ def . 2. of this ] the fine of half of the arc EA . Which was to be found . PROP . XI . PROB . Fig . 10 . 26. AB and EF , the fines of the given arcs KB and KF ...
Other editions - View all
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.