Elements of analytical geometry and the differential and integral calculus . > for the equation sought. Scholium 1. To find where the normal cuts the axis of X,we must make y=0, then we shall have. -i^-i^y-- Application.—Meridians on the earth are ellipses; the semi-major axis through the equator is ^=3963. miles, and the semi-minor axis from the center to the pole is J5= A plumb line is everywhere at right angles to the surface, andof course its prolongation would be a normal line like PuV. Inlatitude 42°, what is the deviation of a plumb line from the centerof the earth? Or, how fa
Elements of analytical geometry and the differential and integral calculus . > for the equation sought. Scholium 1. To find where the normal cuts the axis of X,we must make y=0, then we shall have. -i^-i^y-- Application.—Meridians on the earth are ellipses; the semi-major axis through the equator is ^=3963. miles, and the semi-minor axis from the center to the pole is J5= A plumb line is everywhere at right angles to the surface, andof course its prolongation would be a normal line like PuV. Inlatitude 42°, what is the deviation of a plumb line from the centerof the earth? Or, how far from the center of the earth would aplumb line meet the plane of the equator? Or, what would bethe value of CiY? As this ellipse is very near a circle, we may take CH for thecosine of 42°, which must be represented by x. This beingassumed, we have a;=2940. (^!^!-) ,+miles CJ}f. Am, THE ELLIPSE. |8 Scholium 2. To find NR, the subnormal^ we simply subtractCiVfrom CR, whence NR=x^(^!:^l\x^=^.\ A^ / A^ We can also find the subnormal from the proportional trianglesFRT, PNR, thus: TR : RP :: RP : RN. ~:^ : y :: y : —NR. Whence iV72=_^. PROPOSITIOl^ VIIL Z^w^s drawn from the foci
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Keywords: ., bookauthorrobinson, bookcentury1800, bookdecade1850, bookyear1856
