A Treatise on Mensuration, Both in Theory and Practice |
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Page 138
... zone ABFE ; and this being taken from the femicircle LADBF , will leave the area of the fegment ADB , as in the rule . And this will converge very fast when x is fmall , or the fegment large . x Corol . When becomes equal to r , the zone ...
... zone ABFE ; and this being taken from the femicircle LADBF , will leave the area of the fegment ADB , as in the rule . And this will converge very fast when x is fmall , or the fegment large . x Corol . When becomes equal to r , the zone ...
Page 144
... of a fimilar fegment in the table , whofe arca let be called a . Then 12 dd :: a : add the area of [ the fegment whofe and diameter d , as in the rule . height is PROBLEM XI . To find the Area of the Zone 144 [ Part 2 . CIRCULAR SEGMENT .
... of a fimilar fegment in the table , whofe arca let be called a . Then 12 dd :: a : add the area of [ the fegment whofe and diameter d , as in the rule . height is PROBLEM XI . To find the Area of the Zone 144 [ Part 2 . CIRCULAR SEGMENT .
Page 145
... zone required . E D Q AR T AB S P Ο 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 RTPQ ; then QTTP , because AR 2 AD ...
... zone required . E D Q AR T AB S P Ο 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 RTPQ ; then QTTP , because AR 2 AD ...
Page 146
... zone required . EXAMPLE II . greater chord AB to be 20 , the lefs DC 15 , and their distance PQ 17. Required the area of the zone ABCD . E D Q GR T O P B F Here , as in the laft example , TO = PA + DOX AP 2 PQ DQ = 35 × 5 2 × 2 × 35 = 4 ...
... zone required . EXAMPLE II . greater chord AB to be 20 , the lefs DC 15 , and their distance PQ 17. Required the area of the zone ABCD . E D Q GR T O P B F Here , as in the laft example , TO = PA + DOX AP 2 PQ DQ = 35 × 5 2 × 2 × 35 = 4 ...
Page 147
... zone RULE II . To the area of the trapezoid ADQP , add that of the fmall fegment 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 to be found ...
... zone RULE II . To the area of the trapezoid ADQP , add that of the fmall fegment 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 to be found ...
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Common terms and phrases
abfcifs againſt alfo altitude angle area fine area bafe baſe becauſe breadth bung cafe cafk circle whofe circumference cofine cone confequently conjugate Corol corollary correfponding curve defcribe dimenfions diſtance divided divifion draw ellipfe equal expreffed faid fame example fcale fecond fection feet fegment feries fhall fides figure fince find the area firft firſt fixed axe fluxion folid fome fphere fpheroid fpindle fquare fruftum ftands ftation fubtract fuch fuppofing furface gallons girt given half head diameter hence hoof hyperbola inches inftrument interfecting laft problem laſt 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 tranfverfe trapezium ufed uſed Verf whofe height whole whoſe
Popular passages
Page 535 - ... being entirely dependent on them, and therefore they should be taken of as great length as possible ; and it is best for them to run along some of the hedges or boundaries of one or more fields, or to pass through some of their angles. All things being determined for these stations, you must take more inner stations, and continue to divide and subdivide, till at last you come to single fields ; repeating the same work for the inner stations as for the outer ones, till the whole is finished.
Page 91 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.
Page 2 - A Right Angle is that which is made by one line perpendicular to another. Or when the angles on each side are equal to one another, they are right angles.
Page 614 - ... for the double row of slates at the bottom, or for how much one row of slates or tiles is laid over another. When the roof is of a true pitch, that is, forming a right angle at top ; then the breadth of the building, with its half added, is the girt over both sides nearly.
Page 617 - The length of a room being 20 feet, its breadth 14 feet 6 inches, and height 10 feet 4 inches ; how many yards of painting are in it, deducting a...
Page 6 - A quadrant, or quarter of a circle, is a sector, having a quarter of the circumference for its arc, and the two radii are perpendicular to each other, as G.
Page 608 - Chimneys are commonly measured as if they were solid, deducting only the vacuity from the hearth to the mantle, on account of the trouble of them. All windows, doors, &c, are to be deducted out of the contents of the walls in which they are placed.
Page 62 - From the edge of a ditch 18 feet wide, surrounding a fort, I took the angle of elevation of the top of the wall and found it 62° 40...
Page 7 - The Measure of an angle, is an arc of any circle contained between the two lines which form that angle, the angular point being the centre ; and it is estimated by the number of degrees contained in that arc.
Page 461 - Ans. the upper part 13'867. the middle part 3 '605. the lower part 2-528. QUEST. 48. A gentleman has a bowling green, 300 feet long, and 200 feet broad, which he would raise 1 foot higher, by means of the earth to be dug out of a ditch that goes round it : to what depth must the ditch be dug, supposing its breadth to be every where 8 feet i Ans. 7f-| feet. QUEST. 49. How high above the earth must a person be raised, that he may see j. of its surface ? Ans. to the height of the earth's diameter.