A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well as Private Tuition, Volume 1Samuel Campbell, Evert Duyckinck, T. & J. Swords, 1816 - Mathematics |
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Page 421
... Frustum of a regular Pyramid or Cone ; being the lower part when the top is cut off by a plane parallel to the base . ADD together the perimeters of the two ends , and multi- ply their sum by the slant height , taking half the product ...
... Frustum of a regular Pyramid or Cone ; being the lower part when the top is cut off by a plane parallel to the base . ADD together the perimeters of the two ends , and multi- ply their sum by the slant height , taking half the product ...
Page 423
... Frustum of a Cone or Pyramid . ADD into one sum , the areas of the two ends , and the mean proportional between them : and take of that sum for a mean area ; which being multiplied by the perpendicu lar height or length of the frustum ...
... Frustum of a Cone or Pyramid . ADD into one sum , the areas of the two ends , and the mean proportional between them : and take of that sum for a mean area ; which being multiplied by the perpendicu lar height or length of the frustum ...
Page 424
... frustum are circles or regular polygons . In this latter case , square one side of each poly- gon , and also multiply the one side by the other ; add all these three products together ; then multiply their sum by the tabular area proper ...
... frustum are circles or regular polygons . In this latter case , square one side of each poly- gon , and also multiply the one side by the other ; add all these three products together ; then multiply their sum by the tabular area proper ...
Page 425
... frustum , the alti- tude being 18 , the greatest diameter 8 , and the least dia- meter 4 . Ans . 527-7888 . Ex . 4. What is the solidity of the frustum of a cone . the altitude being 25 , also the circumference at the greater end ...
... frustum , the alti- tude being 18 , the greatest diameter 8 , and the least dia- meter 4 . Ans . 527-7888 . Ex . 4. What is the solidity of the frustum of a cone . the altitude being 25 , also the circumference at the greater end ...
Page 426
... frustum , multiply the whole circumference of the sphere by the height of the part required . Ex . 1. Required the convex superficies of a sphere , whose diameter is 7 , and circumference 22 . Ans . 154 . Ex . 2. Required the ...
... frustum , multiply the whole circumference of the sphere by the height of the part required . Ex . 1. Required the convex superficies of a sphere , whose diameter is 7 , and circumference 22 . Ans . 154 . Ex . 2. Required the ...
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Common terms and phrases
ABCD abscisses ac² altitude arithmetical arithmetical progression axis base bisected CA² CD² centre chord circle circumference common compound cone consequently cube root cubic equation cylinder decimal denominator denotes diameter difference distance divide dividend divisor draw equal angles equal th equation equiangular equilateral EXAMPLES feet figure fraction frustum geometrical progression given number gives greater Hence improper fraction inches infinite series inscribed length Let ABC logarithm manner measured by half multiply ordinates parallel parallelogram perpendicular plane polygon prism PROBLEM proportional Q. E. D. Corol Q. E. D. THEOREM quantity QUEST quotient radii radius ratio rectangle Reduce right angles right line right-angled triangle rule side AC sine square root subtract surd tangent theor theref transposing triangle ABC VULGAR FRACTIONS whole number yards
Popular passages
Page 6 - Los números cardinales 0: zero 1: one 2: two 3: three 4: four 5: five 6: six 7: seven 8: eight 9: nine 10: ten 11: eleven 12: twelve 13: thirteen 14: fourteen 15: fifteen 16: sixteen 17: seventeen 18: eighteen 19: nineteen 20: twenty...
Page 285 - AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side.
Page 438 - 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 187 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 202 - Subtract its power from that term, and bring down the second term for a dividend. 3. Involve the root, last found, to the next lowest -power, and multiply it by the index of the given power for a divisor.
Page 290 - A perpendicular is the shortest line that can be drawn from a given point to a given line.
Page 86 - Then say, by the rule of three, as the sum of the given number and double the assumed cube is to the sum of the assumed cube and double the given number, so is the root of the assumed cube to the root required, nearly ; Or as the first sum is to the difference of the given and assumed...
Page 398 - Two ships of war, intending to cannonade a fort, are, by the shallowness of the water, kept so far from it, that they suspect their guns cannot reach it with effect. In order, therefore, to measure the distance, they separate from each other a quarter of a mile, or 440 yards ; then each ship observes and measures the angle which the other ship and the fort subtend, which angles are 83° 45
Page 355 - B draw chords BA, BC, to the two other points, and bisect these chords perpendicularly by lines meeting in O, which will be the centre. Then from the centre O, at the distance of any one of the points, as ( ) A, describe a circle, and it will pass through the two other points B, C, as required.
Page 56 - To reduce an improper fraction to a whole, or mixed number. Divide the numerator by the denominator, and the quotient will be the whole, or mixed number required.