A Treatise on Mensuration: Both in Theory and PracticeSaint, 1770 - 646 pages |
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Page 14
... Wherefore in a right- angled triangle , the one acute angle being fubtracted from 90 ° , the remainder will be the other ; and the fum of any two angles of a triangle being taken from 180 ° , will leave the third angle . In a right ...
... Wherefore in a right- angled triangle , the one acute angle being fubtracted from 90 ° , the remainder will be the other ; and the fum of any two angles of a triangle being taken from 180 ° , will leave the third angle . In a right ...
Page 21
... Wherefore we have only to prove that the fum of the fines is to the difference of the fines of two arcs , as the tangent of half the fum of thofe arcs is to the tangent of half their diffe- rence : In order to which , let BD , CE , be ...
... Wherefore we have only to prove that the fum of the fines is to the difference of the fines of two arcs , as the tangent of half the fum of thofe arcs is to the tangent of half their diffe- rence : In order to which , let BD , CE , be ...
Page 59
... to the length and perpendicular height of the latter . Wherefore the area of every parallelogram is equal to the product of its length and height . 2.E.D. Note . Becaufe that the length of a fquare is Sect . I , 59 PLANE FIGURES .
... to the length and perpendicular height of the latter . Wherefore the area of every parallelogram is equal to the product of its length and height . 2.E.D. Note . Becaufe that the length of a fquare is Sect . I , 59 PLANE FIGURES .
Page 64
... Wherefore , by the rule , 40x14 * 52368 2 = 20x14.52368 = 290 4736 fquare chains , or 29'04736 acres 4 • 18944 40 7'57760 - --- - Anf . 29 ac . 7 per . EXAMPLE II . How many fquare feet are in a right- angled triangle whose base is 40 ...
... Wherefore , by the rule , 40x14 * 52368 2 = 20x14.52368 = 290 4736 fquare chains , or 29'04736 acres 4 • 18944 40 7'57760 - --- - Anf . 29 ac . 7 per . EXAMPLE II . How many fquare feet are in a right- angled triangle whose base is 40 ...
Page 73
... the other extreme and mean ; and confequently the four remainders will be equal to the four given fides . Wherefore , & c.- That is , abcd = the area . nually together , and the square root of the last Sect . 73 PLANE FIGURES .
... the other extreme and mean ; and confequently the four remainders will be equal to the four given fides . Wherefore , & c.- That is , abcd = the area . nually together , and the square root of the last Sect . 73 PLANE FIGURES .
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abfciffa againſt alfo Alnwick alſo altitude angle area Verf bafe baſe becauſe breadth bung cafe cafk circle whofe circumference cofine cone confequently conftruction conjugate COROLLARY defcribe difference dimenfions diſtance ditto divided divifion ellipfe equal expreffed expreffion faid fame example fecond fection feet fegment feries fhall fide figure fimilar fince find the area firſt fixed axe fluxion folid fome fpheroid fpindle fquare fruftum fubtract fuch fuppofing furface gallons girt greateſt half head diameter hence hoof hyperbola inches interfecting laft laſt laſt problem lefs length meaſure method middle moſt multiply muſt Newcaſtle oppofite ordinate parabola paraboloid parallel perpendicular plane prob quotient radius rule Schoolmafter ſhall Sliding Rule ſphere ſquare ſtation tangent theſe thickneſs thofe thoſe tranfverfe trapezium triangle uſed vertex Wherefore whofe whofe height whole whoſe zone ΙΟ