# Mechanics applied to engineering, Edition: 8th ed by John Goodman By John Goodman

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X 4 the properties of the parabola, V area of strip = B h db . = B* ( —- ) V B* ^ ^ = ""-M^ t^i we have r- B H= than 4 Mechanics applied 32 to Engineering. bd Surfaces bounded by an irregular curve. = — Area of figure areas of parabolic segments (a b-\rC-\-d-\-e) areas of triangles {g K). + + Fig. 32. Mean ordinate method. Area of figure = (/« + Aj + ^ + hi Fio. 33. )a: Mensuration. 33 = The area abc f area of triangle abd, hence the remainder \ of triangle abd. Simply a case of addition and subtraction of areas.

Figure = bh 9a Trapezium, -A. Area of figure Fig. = ( j li «. Irrtgular straight-linedfigure. , 6 = Area of figure area ahdef — area 3frf or area of triangles (acb-^acf-\-cfe->rced) Fig. »9* Mensuration. " 27 The proof is somewhat lengthy, but Longmans' Mensuration," p. 18). Area of upper triangle perfectly simple (see =— -' 2 „ lower triangle =— - 2 both triangles = b( ^l±Jh \ = bh 2 Aiea. of parallelogram Area of triangle = = 61/1 \ ~ " 2 Area of whole figure = (^ - '^1 + ^'^)^ = iA±m 2 Simple case of addition and subtraction of areas.

R,a. x3. /^ ir^+ 2(D ^ A -d)- 4D ^^ d)'- V(D+rf)(D + 2rf) Mensuration. 23 The length of lines can be measured to within -^ in. with a scale divided into either tenths or twentieths of an inch. With special appliances lengths can be measured to within ' 1000000 in. if necessary. The mathematical process by which the value of ir is detertoo long for insertion here. One method consists of calculating the perimeter of a many-sided polygon described about a circle, also of one bscribed in a circle.