पृष्ठम्:लघुभास्करीयम्.djvu/१२९

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एतत् पृष्ठम् अपरिष्कृतम् अस्ति


56 the middle of the sky), the Rsine of the sum or difference of the arcs of the latitude and the (Sun's).declimation according as the Sun is in the southern or morthern hemisphere, is the (great) shadow. Whatever is the sguare root of the number which is obtained on subtracting the square of that fro1 the square of the radius is the (great) grnommon. The shadow of the gnommon of twelve (aigulds) should be determined by proportion. The great shadow is the Rsine of the Sun's zernith distance, and the great gnommon is the Rsine of the Sun's altitude . When the great shadow and the great grnormon are known, the shadow of the gnommon of twelve aigulas is obtained by the formula: great shadow x 12 shadow of the gnommon= great A rule for the determination of the Sun's longitude from the midday shadow of the gnommon 29-33. The sguare root of the sum of the squares of the grommon and its midday shadow is the divisor of the product of the (midday) shadow. and the radius: the resulting quotient is the Rsine of the (Sun's) meridian Zermith distance. (When the midday shadow falls) towards the north, the Sun's meridian 2emith distance, if less than the latitude, should be subtracted from the latitude; when the (midday) shadow falls towards the south, take their sum: the result (in b0th cases) is the (Sun's northern) declimation. * In the contrary case (i.., when the midday shadow falls towards the north but the Sun's meridian zernith distance is greater than the latitude), the latitude should be subtracted from the(Sun's) meridian 2emith distance the (resulting) remainder is the Sun's southern declination.* The Rsine of that (i.e., the Sun's declimation, north or south) should be multiplied by the radius and divided by the (Sun's) greatest declination: the arc corresponding to the quotient or that