A treatise on mensuration, both in theory and practice. The second edition, with many additionsG. G. J.&J. Robinson, 1788 - 16 pages |
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Page 138
... zone ABFE ; and this being taken from the femicircle EADBF , will leave the area of the fegment AD B , as in the rule . And this will converge very fast when x is fmall , or the fegment large . Corol . When becomes equal to r , the zone ...
... zone ABFE ; and this being taken from the femicircle EADBF , will leave the area of the fegment AD B , as in the rule . And this will converge very fast when x is fmall , or the fegment large . Corol . When becomes equal to r , the zone ...
Page 144
... fimilar segment in the table , whose area let be called a . Then r2 : dd :: a : add the area of [ the fegment whofe height is and diameter d , as in the rule . V PROBLEM XI . To find the Area of the Zone 144 [ Part 2 . CIRCULAR SEGMENT .
... fimilar segment in the table , whose area let be called a . Then r2 : dd :: a : add the area of [ the fegment whofe height is and diameter d , as in the rule . V PROBLEM XI . To find the Area of the Zone 144 [ Part 2 . CIRCULAR SEGMENT .
Page 145
... zone required . D E A S OE PO Q T B EXAMPLE I. Suppofe the greater chord AB be 96 , the lefs chord Dc 60 , and the distance PQ between them 26 ; required the area . Draw AD , and let Ds be 1 AP , OR 1 AD , and RTPQ ; then QT TP ...
... zone required . D E A S OE PO Q T B EXAMPLE I. Suppofe the greater chord AB be 96 , the lefs chord Dc 60 , and the distance PQ between them 26 ; required the area . Draw AD , and let Ds be 1 AP , OR 1 AD , and RTPQ ; then QT TP ...
Page 146
... zone required . EXAMPLE II . Suppose the greater chord AB to be 20 , the less DC 15 , and their diftance PQ 171 . area of the zone ABCD . Required the GR FOA F Here , as in the laft example , B PA + DOX AP DQ TO = = 2 PQ 35 × 5 = 2 × 2 ...
... zone required . EXAMPLE II . Suppose the greater chord AB to be 20 , the less DC 15 , and their diftance PQ 171 . area of the zone ABCD . Required the GR FOA F Here , as in the laft example , B PA + DOX AP DQ TO = = 2 PQ 35 × 5 = 2 × 2 ...
Page 147
... zone ABCD required . RULE II . To the area of the trapezoid ADQP , add that of the small segment AGDKA , and double the fum will be the area of the zone ABCD required . — And this rule is easier than the other , as only one fegment is ...
... zone ABCD required . RULE II . To the area of the trapezoid ADQP , add that of the small segment AGDKA , and double the fum will be the area of the zone ABCD required . — And this rule is easier than the other , as only one fegment is ...
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Common terms and phrases
abfcifs againſt alfo altitude angle area fine area bafe baſe becauſe breadth bung cafe cafk chains circle whofe circumference cofine cone confequently conjugate Corol corollary curve defcribe diagonal dimenfions diſtance divided divifion draw ellipfe equal expreffed expreffion faid fame example fecond fection feet fegment feries fhall fides figure fimilar fince find the Area firft firſt fluxion folid fome fphere fpheroid fpindle fquare fruftum ftands ftation fubtract fuch fuppofing furface gallons given greateſt half hence hoof hyperbola inches inftrument inſtead interfecting laft laſt problem lefs length meaſure multiply muſt nearly oppofite ordinate parabola paraboloid parallel perpendicular plane prob quotient radius rule SCHOLIUM ſhall Sliding Rule tangent thefe theſe thofe thoſe tranfverfe trapezium triangle uſed Verf whofe whofe height whole whoſe ΙΟ