S U R 



SUN'S parallax m altitude. 



SURFACES of Solids. 



Let# ordinate of any curve, z length ; then 

 Surface fl. 2 v ydz. 



Ex. 1. Surface of cone = 2 s- 6 X , where b = base, and * = slant 

 side, circumference of base X | slant side. 



2. Surface of sphere 4 a- r* = four times the area of one of its great 

 circles. 



S. Sorface of paraboloid = 



6 ' 





4. Surface of cycloid = 5 (a diameter of generating circle.) 



Guldinus' property. 



Let M D E K (see Fig. Art. Solid} be any plane figure, revolving about 

 an axis xy in its own plane j then the area of the suriace generated by 

 the perimeter of this figure, is equal to the circumference described by 

 the centre of gravity of the perimeter multiplied into the perimeter. 



Ex. Let D M E K be a circle, then the solid will represent the ring of 

 an anchor, arid if r radius of circle, and a = A O, the surface = 2 * a 

 X2rr = 4- 8 ar. 



SURVEYING. 



I. Surveying Land. 



1. The area of a triangle =: base X | perppndirular altitude : or -=; th* 

 product of any two sides X natnr.il sine of their included / ; or when 

 three aides A B, AC, B C arc given, tlieir half sum being S are* = 



J s X (S A B) X (S A C) X (S BC)] 

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