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 298
... rect- angles EF , FB . That is , the square of AB is equal to the squares of AC , CB , together with twice the rectangle of Ac , to CB . CB QE . D. Corol . Hence , if a line be divided into two equal parts ; the square of the whole line ...
... rect- angles EF , FB . That is , the square of AB is equal to the squares of AC , CB , together with twice the rectangle of Ac , to CB . CB QE . D. Corol . Hence , if a line be divided into two equal parts ; the square of the whole line ...
Page 301
... two extremes of the base , or equal to the rect- angle of the base and the difference or sum of the segments , according as the perpendicular falls within or without the triangle , That That is . AC + BC AC BC = AD THEOREMS . 301.
... two extremes of the base , or equal to the rect- angle of the base and the difference or sum of the segments , according as the perpendicular falls within or without the triangle , That That is . AC + BC AC BC = AD THEOREMS . 301.
Page 315
... Rect- angle of the Parts of the one , is Equal to the Rectangle of the Parts of the other ; the Parts of each being measured from the point of meeting to the two intersections with the circumference . LEF LET the two lines , AB , CD ...
... Rect- angle of the Parts of the one , is Equal to the Rectangle of the Parts of the other ; the Parts of each being measured from the point of meeting to the two intersections with the circumference . LEF LET the two lines , AB , CD ...
Page 318
... Rect angles of the Opposite Sides . LET ABCD be any quadrilateral inscribed in a circle , and AC , BD , its two diagonals : then the rectangle AC . BD is the rect- angle AB . DC + the rectangle AD . BC . For , let cE be drawn , making ...
... Rect angles of the Opposite Sides . LET ABCD be any quadrilateral inscribed in a circle , and AC , BD , its two diagonals : then the rectangle AC . BD is the rect- angle AB . DC + the rectangle AD . BC . For , let cE be drawn , making ...
Page 319
... rect . AD . BC + the rect . AB . DC ( ax . 1 ) , 1040 OF RATIOS AND PROPORTIONS . Q. E. D. DEFINITIONS . DEF 76. RATIo is the proportion or relation which one magnitude bears to another magnitude of the same kind with respect to ...
... rect . AD . BC + the rect . AB . DC ( ax . 1 ) , 1040 OF RATIOS AND PROPORTIONS . Q. E. D. DEFINITIONS . DEF 76. RATIo is the proportion or relation which one magnitude bears to another magnitude of the same kind with respect to ...
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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.