A Treatise on Mensuration: Both in Theory and Practice
T. Saint, 1770 - 646 pages
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abſciſſa alſo altitude angle baſe becomes bung caſk circle circular circumference cone conjugate conſequently COROLLARY curve DEMONSTRATION deſcribed diameter difference diſtance divided double draw drawn ellipſe ends equal evident EX A M P L EXAMPLE feet fide figure firſt fixed folidity fruſtum gallons give given greater half head height hence hoof hyperbola inches infinite John laſt length leſs mean meaſure method middle multiply nearly Note ordinate parabola parallel perpendicular plane prob PROBLEM proportional putting pyramid quantity quotient radius remainder root rule ſaid ſame Schoolmaſter ſection ſegment ſeries ſhall ſide ſimilar ſine ſolid ſphere ſpheroid ſpindle ſquare ſum ſurface taken theſe thoſe triangle uſed verſed Wherefore whole whoſe whoſe height zone
Page 549 - AG-at 18'95, the wine and ale gage points, to make this instrument serve the purpose of a gaging rule. On the other part of this face, there is a table of the value of a load, or 50 cubic feet, of timber, at all prices, from, 6 pence to 2 shillings a foot. When 1 at the beginning of any line is accounted...
Page 427 - 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.
Page 86 - ... himself closely to the measuring of them, as well as other figures. Accordingly he determined the relations of spheres, spheroids, and conoids to cylinders and cones ; and the relations of parabolas to rectilineal planes, whose quadratures had long before been determined by Euclid. He has left us also his attempts upon the circle ; he proved that a circle is equal to a right...
Page 86 - In his time the conic sections were admitted into geometry, and he applied himself closely to the measuring of them as well as other figures. Accordingly he determined the relations of spheres, spheroids, and conoids, to cylinders and cones ; and the relations of parabolas to rectilineal planes, whose quadratures had long before been determined by Euclid. He has...
Page 159 - Add into one sum the areas of the two ends, and the mean proportional between them...
Page 163 - To the sum of the areas of the two ends add four times the area of a section parallel to and equally distant from both ends, and this last sum multiplied by | of the height will give the solidity.
Page 216 - An Absciss is a part of any diameter contained between its vertex and an ordinate to it; as AK or BK, • DN or EN.
Page 86 - ... triangle, whose base is equal to the circumference, and its altitude equal to the radius ; and consequently, that its area is found by drawing the radius into half the circumference; and so reduced the quadrature of the circle to the determination of the ratio of the diameter to the circumference ; but which, however, hath not vet been done.
Page 87 - T, which therefore will be nearly the ratio of the circumference to the diameter. From this ratio of the circumference to the diameter he...
Page 426 - ... to determine what number of glasses a company of 10 persons would have in the contents of it, when filled, using a conical glass, whose depth is 2 inches, and the diameter of its top an inch and a half ? Ans. 114-0444976 glasses each.