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 2W. Hilliard, 1808 - Mathematics |
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Page 3
... frustum is the part , that remains at the bottom , af- ter the segment is cut off . 15. A zone of a sphere is a part , intercepted between two parallel planes ; and is the difference between two segments . When the ends , or planes ...
... frustum is the part , that remains at the bottom , af- ter the segment is cut off . 15. A zone of a sphere is a part , intercepted between two parallel planes ; and is the difference between two segments . When the ends , or planes ...
Page 13
... frustum of a right cone . RULE . * Multiply the sum of the perimeters of the two ends by the slant height or side of the frustum , and half the product will be the surface . NOTE . The same rule may be used to find the surface of the ...
... frustum of a right cone . RULE . * Multiply the sum of the perimeters of the two ends by the slant height or side of the frustum , and half the product will be the surface . NOTE . The same rule may be used to find the surface of the ...
Page 14
... frustum ABCD , E 12'5 10'3 A 22'8 14 A B 912 228 2 ) 319'2 1596 answer , 2. What is the convex surface of the frustum of a cone , the slant height of the frustum being 12'5 , and the circum- ferences of the two ends 6 and 3'4 ? Ans . 90 ...
... frustum ABCD , E 12'5 10'3 A 22'8 14 A B 912 228 2 ) 319'2 1596 answer , 2. What is the convex surface of the frustum of a cone , the slant height of the frustum being 12'5 , and the circum- ferences of the two ends 6 and 3'4 ? Ans . 90 ...
Page 16
... Eg hk , and its correct fluent = Ax , the same as in the cone ; and the same rule is ap- plicable , whatever be the figure of the base . Q. E. D. PROBLEM VIII . To find the solidity of the frustum. 16 MATHEMATICS . Cone, and Pyramid.
... Eg hk , and its correct fluent = Ax , the same as in the cone ; and the same rule is ap- plicable , whatever be the figure of the base . Q. E. D. PROBLEM VIII . To find the solidity of the frustum. 16 MATHEMATICS . Cone, and Pyramid.
Page 17
... frustum of a cone or any pyramid . 1. For the frustum of a cone . RULE . ' Divide the difference of the cubes of the diameters of the two ends by the difference of the diameters , and this quotient , being multiplied by 7854 and again ...
... frustum of a cone or any pyramid . 1. For the frustum of a cone . RULE . ' Divide the difference of the cubes of the diameters of the two ends by the difference of the diameters , and this quotient , being multiplied by 7854 and again ...
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Common terms and phrases
abscisses altitude axis azimuth base Ca² cask centre complement cone conjugate cosine course curve DE³ declination departure describe dial diameter diff difference of latitude difference of longitude distance divide draw the parallel drawn ecliptic ellipse equal equinoctial EXAMPLES feet figure find the rest frustum height Hence horizon hour angle hour lines hyperbola hypotenuse inches intersection LATITUDE SAILING length measure Mercator's meridional difference middle latitude miles multiply NOTE oblique circle opposite ordinates parabola parallel of latitude parallel sailing perpendicular plane sailing pole prime vertical primitive Prob PROBLEM projection Prop proportional Q. E. D. COR quadrant radius rectangle Required the content rhumb right ascension right circle right line rule secant segment Side AC sine sphere spheric triangle spindle square star station Stereographic Projection stile sun's tance tang tangent THEOREM vertical
Popular passages
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 147 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
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 59 - ... 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 61 - 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 63 - 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 62 - 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.
Page 29 - ... -5236, for the content. RULE II. To 3 times the square of the radius of the segment's base, add the square of its height ; then multiply the sum by the height, and the product by -5236, for the content.