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 1
... Ellipse 402 419 429 457 466 469 473 Of the Hyperbola Of the Parabola 491 514 Of the Conic Sections as expressed by Algebraic equations , called the Equations of the Curve 532 Elements of Isoperimetry . 535 Problems relative to the ...
... Ellipse 402 419 429 457 466 469 473 Of the Hyperbola Of the Parabola 491 514 Of the Conic Sections as expressed by Algebraic equations , called the Equations of the Curve 532 Elements of Isoperimetry . 535 Problems relative to the ...
Page 418
... Ellipse . Otherwise thus . Divide the height of the segment by the vertical axis of the ellipse ; and find , in the table of circular segments to prob . 12 , the circular segment having the above quotient for its versed sine : then ...
... Ellipse . Otherwise thus . Divide the height of the segment by the vertical axis of the ellipse ; and find , in the table of circular segments to prob . 12 , the circular segment having the above quotient for its versed sine : then ...
Page 469
... ellipse when the cone is cut obliquely through both sides , or when the plane is inclined to the base in a less angle than the side of the cone is . 6. The section is a parabola , when the cone is cut by a plane parallel to the side ...
... ellipse when the cone is cut obliquely through both sides , or when the plane is inclined to the base in a less angle than the side of the cone is . 6. The section is a parabola , when the cone is cut by a plane parallel to the side ...
Page 470
... ellipse and the opposite hyperbolas , have each two vertices ; but the parabola only one ; unless we consider the ... Ellipse : Ellipse . Hyperbolas . Parabola . MH TH D M. 470 CONIC SECTIONS .
... ellipse and the opposite hyperbolas , have each two vertices ; but the parabola only one ; unless we consider the ... Ellipse : Ellipse . Hyperbolas . Parabola . MH TH D M. 470 CONIC SECTIONS .
Page 471
... Ellipse . Hyperbolas . Parabola . MH TH D M. D KA A IG Ꮐ I 11. The Centre c is the middle of the axis . Hence the centre of a parabola is infinitely distant from the vertex . And of an ellipse , the axis and centre lie within the curve ...
... Ellipse . Hyperbolas . Parabola . MH TH D M. D KA A IG Ꮐ I 11. The Centre c is the middle of the axis . Hence the centre of a parabola is infinitely distant from the vertex . And of an ellipse , the axis and centre lie within the curve ...
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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.