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 471
... 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 ... Conjugate to any diameter , is the line drawn through the centre , and parallel to the tangent of the curve at the vertex ...
... 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 ... Conjugate to any diameter , is the line drawn through the centre , and parallel to the tangent of the curve at the vertex ...
Page 472
... conjugate hyperbolas to the two former DAE , FBG , and each pair of opposite curves mutually conjugate to the other ; being all cut by one plane , from four conjugate cones , as in page 470 , def . 8 . 19. And if tangents be drawn to ...
... conjugate hyperbolas to the two former DAE , FBG , and each pair of opposite curves mutually conjugate to the other ; being all cut by one plane , from four conjugate cones , as in page 470 , def . 8 . 19. And if tangents be drawn to ...
Page 497
... Hyperbolas are equal to one another , and each equal to the Rectangle of the two Axes . That is , the parallelogram PQRS = the rectangle AB . ab . a g R E B Let EG , eg be two conjugate ... HYPERBOLA . 497.
... Hyperbolas are equal to one another , and each equal to the Rectangle of the two Axes . That is , the parallelogram PQRS = the rectangle AB . ab . a g R E B Let EG , eg be two conjugate ... HYPERBOLA . 497.
Page 503
... conjugate diameters , form a parallelogram inscribed between the hyperbolas , and the pairs of opposite sides are each equal to the corresponding parallel conjugate diameters . - For , if the diameter eh be drawn parallel to the tangent ...
... conjugate diameters , form a parallelogram inscribed between the hyperbolas , and the pairs of opposite sides are each equal to the corresponding parallel conjugate diameters . - For , if the diameter eh be drawn parallel to the tangent ...
Page 507
... conjugate hyperbolas at a ' , q ' . it may be proved that LQLq ' . Or if the tangent TE be produced , then EV = EW . Also the diameter GCEH bisects all lines drawn parallel to TE or q , and limited either by one hyperbola , or by its ...
... conjugate hyperbolas at a ' , q ' . it may be proved that LQLq ' . Or if the tangent TE be produced , then EV = EW . Also the diameter GCEH bisects all lines drawn parallel to TE or q , and limited either by one hyperbola , or by its ...
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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.