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adjacent alſo angle ABC angle ACB angle BAC angle BCA baſe becauſe called caſe centre chord circle circumference cofine common complement conſtructed coſine deſcribed diameter difference diſtance divided diviſions draw drawn equal equator Example extremes fide fide AC figure fine firſt fourth proportional geometrical plane given greater Hence hypothenuſe inclination join laſt latitude leſs likewiſe lines of fines loga logarithm manner mean meaſure meeting middle minutes oppoſite parallel parallel diſtance perpendicular perſpective plane Plate pole primitive projected PROP propoſition quadrant radius rectangle contained remainder right angles rule ſame ſcale ſecond ſect ſection ſector ſeries ſhadow ſhall ſide ſphere ſpherical angle ſquare ſtar ſtraight line ſum tables taken tangent THEOR theſe third three terms triangle ABC trigonometry uſe wherefore whoſe
Page 79 - 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 80 - 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 92 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Page 80 - ... 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 162 - If a solid angle be contained by three plane angles, any two of them are together greater than the third.
Page 26 - 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 72 - 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 37 - 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 235 - ... 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.