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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Σελίδα 22
... its most general form by the Newtonian Binomial Theorem . Suppose we were required to raise the binomial a + b to any power denoted by n From the principles already laid down , The first term would be a * . The second 22 ALGEBRA .
... its most general form by the Newtonian Binomial Theorem . Suppose we were required to raise the binomial a + b to any power denoted by n From the principles already laid down , The first term would be a * . The second 22 ALGEBRA .
Σελίδα 42
... both sides of the equation by the co - efficient of x , ( if it has any co - efficient ) and then extract the square root of each side of the equation . Examples . 1. Suppose x + 5 = 54 , 42 ALGEBRA . Quadratic Equations.
... both sides of the equation by the co - efficient of x , ( if it has any co - efficient ) and then extract the square root of each side of the equation . Examples . 1. Suppose x + 5 = 54 , 42 ALGEBRA . Quadratic Equations.
Σελίδα 64
... suppose that 2 is substituted for x in the equation x3 - 3x2 + 5x − 7 = 0 , the result is -1 . For , let the root of the proposed equation be diminished by 2 ; then , by the operation of transformation following , viz . 1-3 5 1 3 1 3 5 ...
... suppose that 2 is substituted for x in the equation x3 - 3x2 + 5x − 7 = 0 , the result is -1 . For , let the root of the proposed equation be diminished by 2 ; then , by the operation of transformation following , viz . 1-3 5 1 3 1 3 5 ...
Σελίδα 99
... suppose the coefficient of the second term of every factor to be b ' , and the coefficient of the second term of their product will be ; whence the first and second terms of their product will be 1 nd mix . If the series 6+ B′x + B′′x2 ...
... suppose the coefficient of the second term of every factor to be b ' , and the coefficient of the second term of their product will be ; whence the first and second terms of their product will be 1 nd mix . If the series 6+ B′x + B′′x2 ...
Σελίδα 105
... Suppose that for every ten sheep a farme kept , he should plough an acre of land , and be allowed one acre of pasture for every four sheep . How many sheep may that person keep who farms 700 acres ? Ans . 2000 . 11. A and B began to ...
... Suppose that for every ten sheep a farme kept , he should plough an acre of land , and be allowed one acre of pasture for every four sheep . How many sheep may that person keep who farms 700 acres ? Ans . 2000 . 11. A and B began to ...
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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.