Mathematics: Compiled from the Best Authors, and Intended to be the Text-book of the Course of Private Lectures on These Sciences in the University at Cambridge, Volume 2
W. Hilliard, 1808 - Mathematics
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abscisses altitude axis azimuth base cask centre circumference complement cone conjugate consequendy cosine course curve declination departure describe dial diameter diff difference of latitude difference of longitude distance divided draw the parallel drawn ecliptic ellipse equal equinoctial EXAMPLES feet figure frustum height Hence horizon hour angle hour lines hyperbola hypotenuse inches intersection LATITUDE SAILING length measure Mercator's middle latitude miles multiply Note oblique circle opposite ordinates parabola parallel of latitude parallel sailing parallelogram perpendicular plane sailing pole prime vertical primitive Prob PROBLEM projection Prop proportional Q. E. D. Cor quadrant radius rectangle Required the content rhumb right angles right ascension right circle right line rule secant segment side sine solidity sphere spheric triangle square star station stile sun's surface tance tang tangent theodolite THEOREM triangle ABC vertical zenith
Page 3 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 8 - Take the length of the keel within board (so much as she treads on the ground) and the breadth within board by the midship beam, from plank to plank, and half the breadth for the depth, then multiply the length by the breadth, and that product by the depth, and divide the whole by 94; the quotient will give the true contents of the tonnage.
Page 61 - ... small statue, the head of which is 97 feet from the summit of the higher, and 86 feet from the top of the lower column, the base of which measures just 16 feet to the centre of the figure's base. Required the distance between the tops of the two columns ? Ans.
Page 63 - A gentleman has a garden 100 feet long, and 80 feet broad ; and a gravel walk is to be made of an equal width half round it ; what must the breadth of the walk be to take up just half the ground? Ans. 25-968 feet.
Page 65 - If a heavy sphere, whose diameter is 4 inches, be let fall into a conical glass, full of water, whose diameter is 5, and altitude 6 inches ; it is required to determine how much water will run over ? AHS.
Page 64 - Ans. the upper part 13'867. the middle part 3 '605. the lower part 2-528. QUES J. 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 ? Ans.
Page 21 - ... 07958 in using the circumferences ; then taking one-third of the product, to multiply by the length, for the content. Ex. 1. To find the number of solid feet in a piece of timber, whose bases are squares, each side of the greater end being 15 inches, and each side of the less end 6 inches ; also, the length or the perpendicular altitude 24 feet.
Page 187 - AC 2AC nearly ; that is, the difference between the true and apparent level is equal to the square of the distance between the places, divided by the diameter of the earth ; and consequently it is always proportional to the square of the distance.