A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for ExerciseG. B. Whittaker, 1825 - 372 σελίδες |
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Αποτελέσματα 6 - 10 από τα 100.
Σελίδα 38
... Given ( F x + jy ++ x = 62 ) 3 - } 3x + y + z 47 it is required to find x , y , and z . y + zx = 38 ) ( { x + First , the given equations , cleared of fractions , become 12x + 8y + 6x = 1488 20x + 15y + 12 % = 2820 30x + 24y + 20x ...
... Given ( F x + jy ++ x = 62 ) 3 - } 3x + y + z 47 it is required to find x , y , and z . y + zx = 38 ) ( { x + First , the given equations , cleared of fractions , become 12x + 8y + 6x = 1488 20x + 15y + 12 % = 2820 30x + 24y + 20x ...
Σελίδα 44
... Given x2 + 6x = 40 to find the value of x . Solu . We know that x2 + 6x + 9 is the square of x + 3 ; for ( x + 3 ) 2 = x2 + 6x + 9 . If , therefore , we add 9 to each side of the equation , there will arise a new equation x2 + 6x + 9 ...
... Given x2 + 6x = 40 to find the value of x . Solu . We know that x2 + 6x + 9 is the square of x + 3 ; for ( x + 3 ) 2 = x2 + 6x + 9 . If , therefore , we add 9 to each side of the equation , there will arise a new equation x2 + 6x + 9 ...
Σελίδα 45
... Given 3r2 + 2x = 33 , to find r . Solu . Divide by 3 , and x2 + Add now the square of the 1 1 co - efficient , namely , X And x + = 3 2 x = 11 . 3 2 1 > then 2+ 9 100 = 10 , extracting the square roo . ; 9 10 1 Therefore , x = - 9 = = 3 ...
... Given 3r2 + 2x = 33 , to find r . Solu . Divide by 3 , and x2 + Add now the square of the 1 1 co - efficient , namely , X And x + = 3 2 x = 11 . 3 2 1 > then 2+ 9 100 = 10 , extracting the square roo . ; 9 10 1 Therefore , x = - 9 = = 3 ...
Σελίδα 79
... Given a 6 , z = 21 , and n = 4 , to find d . asz 21-6 n - 1 = 3 2. Given a = 1 , z = } , and n = 11 , to find d . - 3. Given a = 10 , z = 80 , and n = 9 , to find s . 15 3 = 5. Ans . Ans . T in ( a + x ) = x9 ( 10 + 80 ) = 405 . Ans . 4.
... Given a 6 , z = 21 , and n = 4 , to find d . asz 21-6 n - 1 = 3 2. Given a = 1 , z = } , and n = 11 , to find d . - 3. Given a = 10 , z = 80 , and n = 9 , to find s . 15 3 = 5. Ans . Ans . T in ( a + x ) = x9 ( 10 + 80 ) = 405 . Ans . 4.
Σελίδα 94
... given quantities a and b ; but since by assumption , r + sa we have also their sum expressed in terms of the same given quantities . Hence we have the sum and difference of two quantities given , to find the quantities themselves , vix ...
... given quantities a and b ; but since by assumption , r + sa we have also their sum expressed in terms of the same given quantities . Hence we have the sum and difference of two quantities given , to find the quantities themselves , vix ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal altitude angle ABC angle BAC axis bisected centre circle ABCD circumference co-efficient cone conic section convergency curve cylinder described diameter divided draw equal angles equation equiangular equimultiples factors fluxion fore fraction geometrical progression given straight line gnomon greater Hence hyperbola join less Let ABC magnitudes multiple opposite parabola parallel parallelogram perpendicular plane angles polygon prism produced proportional pyramid Q. E. D. PROP Q. E. D. Proposition radius rectangle rectangle contained rectilineal figure remaining angle right angles segment shewn side BC similar sine solid angle solid parallelopiped spherical triangle square of AC subtract surd tang tangent Theorem third tiple triangle ABC vertex whence Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 172 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Σελίδα 191 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 190 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 196 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 192 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 177 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 209 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 284 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.
Σελίδα 286 - 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. either the sides adjacent to the equal...
Σελίδα 179 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.