A Treatise on Mensuration: Both in Theory and PracticeSaint, 1770 - 646 pages |
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Page 63
... Multiply one of its fides by the perpendicular let upon it from its opposite angle , and half the duct will be the area . ACBP That is , = the area . 2 pro- EXAMPLE I. What is the area of a triangle whose three fides are 20 , 30 , 40 ...
... Multiply one of its fides by the perpendicular let upon it from its opposite angle , and half the duct will be the area . ACBP That is , = the area . 2 pro- EXAMPLE I. What is the area of a triangle whose three fides are 20 , 30 , 40 ...
Page 72
... multiply the fum of these products by half the fine of the angle included by either of the pairs of fides which are multiplied together ; fo fhall this laft product be the area . That is , ADXDC + ABxBCxs . LD or s . LB the last figure ...
... multiply the fum of these products by half the fine of the angle included by either of the pairs of fides which are multiplied together ; fo fhall this laft product be the area . That is , ADXDC + ABxBCxs . LD or s . LB the last figure ...
Page 73
... multiply the four remainders conti- and 1 : √ T Sa : a√1 — ss = ÁS , 26 : 6√1-55 = CT , nually hence SD = d + a1 — ss , and DT = c - b / 1 — ss ; and , by right - angled triangles , BS + SD2 = DT2 + TB2 , that is , dd + 2ad √1 − ss ...
... multiply the four remainders conti- and 1 : √ T Sa : a√1 — ss = ÁS , 26 : 6√1-55 = CT , nually hence SD = d + a1 — ss , and DT = c - b / 1 — ss ; and , by right - angled triangles , BS + SD2 = DT2 + TB2 , that is , dd + 2ad √1 − ss ...
Page 79
... areas of regular figures or polygons . RULE I. Multiply half the perimeter of the figure by the radius of its infcribed circle , or by the perpendicular demitted demitted from its center to one of the fides , Sect . I. 79 REGULAR POLYGONS .
... areas of regular figures or polygons . RULE I. Multiply half the perimeter of the figure by the radius of its infcribed circle , or by the perpendicular demitted demitted from its center to one of the fides , Sect . I. 79 REGULAR POLYGONS .
Page 80
... multiplied by the number of fides . 2. The center of the figure is the fame as the center of the inscribed or ... Multiply the fquare of the fide , of any regu- lar figure , by the multiplier ftanding oppofite to its * For , the ...
... multiplied by the number of fides . 2. The center of the figure is the fame as the center of the inscribed or ... Multiply the fquare of the fide , of any regu- lar figure , by the multiplier ftanding oppofite to its * For , the ...
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Common terms and phrases
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