Key to System of practical mathematics. 2 pt. No.xvii |
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Página 70
... chord parallel to AB , it is required to prove , that if a point F be taken in the dia- meter , and s FC , FD be drawn from it to the extremities of the chord CD , that FC2 + FD2 - FA2 + FB2 . B E F B = Q. E. D. G Through the centre E ...
... chord parallel to AB , it is required to prove , that if a point F be taken in the dia- meter , and s FC , FD be drawn from it to the extremities of the chord CD , that FC2 + FD2 - FA2 + FB2 . B E F B = Q. E. D. G Through the centre E ...
Página 71
... be a circle , and ADE another , described on the radius of the former as its diameter ; any chord AB drawn in the former from the point of contact , will be bisected by the latter . From the centre E of KEY - GEOMETRICAL EXERCISES . 71.
... be a circle , and ADE another , described on the radius of the former as its diameter ; any chord AB drawn in the former from the point of contact , will be bisected by the latter . From the centre E of KEY - GEOMETRICAL EXERCISES . 71.
Página 72
... chord AB ,. ( Prop . 46 ) AB is bisected in D. 24. Let ABC be a triangle , and BD a perpendicular , drawn from B , upon the third side AC ; it is requir- ed to prove that the rectangle AB BC is equal to the rectangle contained by BD ...
... chord AB ,. ( Prop . 46 ) AB is bisected in D. 24. Let ABC be a triangle , and BD a perpendicular , drawn from B , upon the third side AC ; it is requir- ed to prove that the rectangle AB BC is equal to the rectangle contained by BD ...
Página 51
... of the wheel 10 feet ; hence 31831 × 10 = 3.1831 feet , the diameter . PROBLEM VIII . 30.6x8-50.8 ( 1. ) 64.6 . Ans . 25.5 × 8-45 ( 2. ) = 53 . Ans . 3 ( 3. ) 64 + 16-8-94427 , chord of half KEY - MENSURATION OF SURFACES . 51.
... of the wheel 10 feet ; hence 31831 × 10 = 3.1831 feet , the diameter . PROBLEM VIII . 30.6x8-50.8 ( 1. ) 64.6 . Ans . 25.5 × 8-45 ( 2. ) = 53 . Ans . 3 ( 3. ) 64 + 16-8-94427 , chord of half KEY - MENSURATION OF SURFACES . 51.
Página 52
... chord of half the arc . ( 4. ) 8.94427x8-16 3 18.518 . Ans . 144 + 81-15 , the chord of half the arc . 15x8-24 = 32 . Ans . 3 Page 70 . ( 1. ) By Table XI . arc of 40 ° to radius 1 = 6981317 دو وو 9 ° 30 ' " " وو arc of 49 ° 30 ' to ...
... chord of half the arc . ( 4. ) 8.94427x8-16 3 18.518 . Ans . 144 + 81-15 , the chord of half the arc . 15x8-24 = 32 . Ans . 3 Page 70 . ( 1. ) By Table XI . arc of 40 ° to radius 1 = 6981317 دو وو 9 ° 30 ' " " وو arc of 49 ° 30 ' to ...
Términos y frases comunes
a+b+c AABC ABCD acres base binomial theorem bisected centre changing the signs chord circle circumference coefficients collecting the terms completing the square cosec denominator diameter difference distance dividing divisor equal extracting the root feet find the area find the differential fraction given equation gives greater segment half the sum height hence the area hypotenuse inches inverted latitude least common multiple Let ABC Log.cosec logarithm miles Mult Multiply number sought perp perpendicular poles Problem XI Prop question radius rectangle semiperimeter sine slant slant height solidity square root substituting Subt Subtract surf Tabular area tangent Theorem third side transp transposing transposition triangle Trig value of x wherefore whole arc whole surface yards دو
Pasajes populares
Página 74 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 75 - If the vertical angle of a triangle be 'bisected 'by a straight line which also cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 9 - Let x measure у by the units in n, then it will measure cy by the units in nc. 2d. If a quantity measure two others, it will measure their sum or difference. Let a be contained...
Página 15 - ... sin(a + b + c). Again (a) represents the coarse ROM, and bands b and c are two controls of the fine-tuned ROMs so that a < 90°, b < 90 • 2~a and c < 90 • 2~(a + 6). This is shown in Fig. 7-7. Sunderland showed that the trigonometric identity can be written as sin(a + b + c) = sin(a + 6) cos c + cos a cos b sin...
Página 10 - The truth of this rule depends upon these two principles ; 1". If one quantity measure another, it will also measure any multiple of that quantity. Let x measure y by the units in n, then it will measure cy by the units in nc.
Página 139 - Arc, on the Sine and Cosine of an Arc in terms of the Arc itself, and a new Theorem for the Elliptic Quadrant.
Página 137 - The differential of the logarithm of a function is equal to the differential of the function, divided by the function itself.
Página 149 - The pyramid may be conceived to be made up of an infinite number of planes parallel to ABC.
Página 81 - ... sum of any number of quantities is equal to the sum of the corresponding functions of each of these quantities, will be called distributive
Página 86 - We thus derive the following method for multiplying two binomials which have a common first term : The first term of the product is the square of the common first terms of the binomials.