Key to System of practical mathematics. 2 pt. No.xvii |
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Página 11
... becomes the following : - x ( 3d quot . ) 20x + 80x3a + 120x2a2 + 80xa3 + 20a1 Mult . by 4 . 20x + 45x3a + 36x2a2 + 11xa3 35x3a + 84a2a2 + 69xa3 + 20a4 --4x5a- 6x + u2— 4x3a3 — x2a1 — a® -4x5a - 16x1a2-24x3a3-16x2a4-4xa5 4 Mult . by 7 ...
... becomes the following : - x ( 3d quot . ) 20x + 80x3a + 120x2a2 + 80xa3 + 20a1 Mult . by 4 . 20x + 45x3a + 36x2a2 + 11xa3 35x3a + 84a2a2 + 69xa3 + 20a4 --4x5a- 6x + u2— 4x3a3 — x2a1 — a® -4x5a - 16x1a2-24x3a3-16x2a4-4xa5 4 Mult . by 7 ...
Página 13
... becomes a3 - a.x2 23 ; and the second being mul- a2 + ax + x2 tiplied by becomes a2 + ax + x2 ' a3 + a * x + ax2 a3 - 3 - ; and the third re- quires no change ; hence 2a3 + a2x + a2 + 22 + a3 - 23 X x2 - 4x and X x + 4 -16 a3 — ax2 a3 + ...
... becomes a3 - a.x2 23 ; and the second being mul- a2 + ax + x2 tiplied by becomes a2 + ax + x2 ' a3 + a * x + ax2 a3 - 3 - ; and the third re- quires no change ; hence 2a3 + a2x + a2 + 22 + a3 - 23 X x2 - 4x and X x + 4 -16 a3 — ax2 a3 + ...
Página 14
... becomes 1 + x Ꮖ ( 5. ) X m + n m2 - n2 m + n m + n m2 + 2mn + n2 m - n m - n m - n and X m + n m - n m2 - 2mn + n2 m2 + 2mn + n2 m2 2mn + n2 ; but m2 - n2 m2 m2 - n2 m2 + 2mn + n2 m2 + 2mn — n2 4mn m2 - n2 " m2 - n2 ° ( 6. ) X MX m + 1 ...
... becomes 1 + x Ꮖ ( 5. ) X m + n m2 - n2 m + n m + n m2 + 2mn + n2 m - n m - n m - n and X m + n m - n m2 - 2mn + n2 m2 + 2mn + n2 m2 2mn + n2 ; but m2 - n2 m2 m2 - n2 m2 + 2mn + n2 m2 + 2mn — n2 4mn m2 - n2 " m2 - n2 ° ( 6. ) X MX m + 1 ...
Página 15
... becomes 2x2 + x_ ( 2x + 1 ) x = x . 2x + 1 2x + 1 multiplying both numerator and denomi- 1 + aba 3d , 6-1 + ō 63 + 1 nator by ab3 , it becomes ( b + 1 ) ( b - b + 1 ) _b + 1 = abab3ab2- ab2 ( 62 — b + 1 ) at ale x + y 4th , X y 2x X xy2 ...
... becomes 2x2 + x_ ( 2x + 1 ) x = x . 2x + 1 2x + 1 multiplying both numerator and denomi- 1 + aba 3d , 6-1 + ō 63 + 1 nator by ab3 , it becomes ( b + 1 ) ( b - b + 1 ) _b + 1 = abab3ab2- ab2 ( 62 — b + 1 ) at ale x + y 4th , X y 2x X xy2 ...
Página 17
... becomes a3 — x3 — y3 — 3a2x — 3a2y + 3ax2 + 3ay2 — 3x2y — 3xy2 + 6axy . ART . 58 . ( 1. ) The square root of 16 is 4 , of a2 is a , of ba is b2 , of c6 is c3 ;. 16a2b4c6-4ab2c3 . ( 2. ) The cube root of 64 is 4 , of a3 is a , of x9 is ...
... becomes a3 — x3 — y3 — 3a2x — 3a2y + 3ax2 + 3ay2 — 3x2y — 3xy2 + 6axy . ART . 58 . ( 1. ) The square root of 16 is 4 , of a2 is a , of ba is b2 , of c6 is c3 ;. 16a2b4c6-4ab2c3 . ( 2. ) The cube root of 64 is 4 , of a3 is a , of x9 is ...
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.