Elemento of Geometry, Theoretical and Practical: Containing a Full Explanation of the Construction and Use of Tables, and a New System of SurveyingPratt, Woodford & Company, 1848 - 324 σελίδες |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 11
... Changing the sign of a factor - Powers .... 8. Square of polynomial , binomial , residual - Product of sum and dif- ference . .... 9. Changing the sign of a polynomial ......... . ....... 10. Degree of product , multiplication and ...
... Changing the sign of a factor - Powers .... 8. Square of polynomial , binomial , residual - Product of sum and dif- ference . .... 9. Changing the sign of a polynomial ......... . ....... 10. Degree of product , multiplication and ...
Σελίδα 30
... changing the sign of a factor changes the sign of the product into which it enters . = Thus and and • + x • + y • + z • ... = + xyz ... 9 - -x • + y == xyz - • ... -x • —y • + z • - - y • ... ... ... = - = + ( xy ) • + z • = ... + ( xyz ) ...
... changing the sign of a factor changes the sign of the product into which it enters . = Thus and and • + x • + y • + z • ... = + xyz ... 9 - -x • + y == xyz - • ... -x • —y • + z • - - y • ... ... ... = - = + ( xy ) • + z • = ... + ( xyz ) ...
Σελίδα 31
... changing the sign of b in ( 8 ) we have or ( 63 ) , ( 6 ) , ( a - b ) 2 = a2 + ( − b ) 2 + 2a ( − b ) , ( a - b ) 2 = a2 + b2 - 2ab . ( 9 ) PROPOSITION VIII . The product of the sum and difference of two quantities ( 10 ) is equal to ...
... changing the sign of b in ( 8 ) we have or ( 63 ) , ( 6 ) , ( a - b ) 2 = a2 + ( − b ) 2 + 2a ( − b ) , ( a - b ) 2 = a2 + b2 - 2ab . ( 9 ) PROPOSITION VIII . The product of the sum and difference of two quantities ( 10 ) is equal to ...
Σελίδα 32
... changing a , into a , b , into - b , we get 2 - ( a + b ) ( a - b ) = a2 — b2 , ) a2b2 = ( a + b ) ( a - b ) . S ( 10 ) Q. What relation does ( 5 ) bear to ( 7 ) ? ( 7 ) to ( 8 ) ? ( 8 ) to ( 9 ) ? ( 56 ) to ( 10 ) ? Which is the more ...
... changing a , into a , b , into - b , we get 2 - ( a + b ) ( a - b ) = a2 — b2 , ) a2b2 = ( a + b ) ( a - b ) . S ( 10 ) Q. What relation does ( 5 ) bear to ( 7 ) ? ( 7 ) to ( 8 ) ? ( 8 ) to ( 9 ) ? ( 56 ) to ( 10 ) ? Which is the more ...
Σελίδα 34
... changing the sign ( 11 ) . ( 11 ) . } + a3b― a2b2 + a2b2 + a2b2 — ab3 + ab3 - b4 + ab3 - b1 5 ° . Divide a b5 , a® — bo , a " -b " , ... , a " -b " , by a - b . - PROPOSITION XI . 10. Multiplying the dividend while the divisor remains ...
... changing the sign ( 11 ) . ( 11 ) . } + a3b― a2b2 + a2b2 + a2b2 — ab3 + ab3 - b4 + ab3 - b1 5 ° . Divide a b5 , a® — bo , a " -b " , ... , a " -b " , by a - b . - PROPOSITION XI . 10. Multiplying the dividend while the divisor remains ...
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Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Theoretical and Practical: Containing a Full ... George Clinton Whitlock Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Elements of Geometry, Theoretical and Practical: Containing a Full ... George Clinton Whitlock Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ abscissa algebraical altitude axis base becomes BINOMIAL THEOREM bisecting C₁ centre chains chord circle circumference coefficients computation constant continuous function cosc cosine cota curve D₂ denominator denote determine diameter difference diminished distance divided division divisor draw drawn ellipse equal equation exponent factors find the derivative fraction function geometry given greater horizontal Hyperbola hypothenuse increment intersect logarithm measured minus multiplied observe operation opposite parabola parallel parallelogram perpendicular plane polygon polynomial problem proportional PROPOSITION quantities quotient radii radius ratio rectangle right angled triangle Scholium secant secant line segments sine sinx square straight line subtangent subtracting tana tanb tangent theorem variable vertical whence y₁
Δημοφιλή αποσπάσματα
Σελίδα 13 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 264 - ... greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle, shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to...
Σελίδα 217 - Through a given point to draw a line parallel to a given straight line.
Σελίδα 195 - As the sine of the angle opposite the given side, is to the sine of the angle opposite the required side ; so is the given side to the required side.
Σελίδα 197 - To find the other side: — • as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference...
Σελίδα 170 - The sine of an arc is the perpendicular let fall from one extremity of the arc on the diameter which passes through the other extremity.
Σελίδα 45 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Σελίδα 83 - ... by four times the square of the line joining the middle points of the diagonals.
Σελίδα 304 - N. by E. NNE NE by N. NE NE by E. ENE E. by N. East E. by S. ESE SE by E. SE SE by S.
Σελίδα 177 - The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference.