A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for Exercise |
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Page 19
... square , cube , biquadrate , & c . of any given quantity or root . Obs . These operations may be easily performed upon small numbers and simple algebraic quantities , as will appear from the mere inspection of the following tables ...
... square , cube , biquadrate , & c . of any given quantity or root . Obs . These operations may be easily performed upon small numbers and simple algebraic quantities , as will appear from the mere inspection of the following tables ...
Page 20
... square of 3x2 + 2x + 5 . the square of a + 2x . the cube of 3x- - 5 . the square of x + y + v . the cube of 6x2y2 + 12xy . the square of x2 - ys + z . + cs . the 5th power of a3 + Ans . 8a " . Ans . 16a x * . Ans . —512 x®y® . ' ( 50 ...
... square of 3x2 + 2x + 5 . the square of a + 2x . the cube of 3x- - 5 . the square of x + y + v . the cube of 6x2y2 + 12xy . the square of x2 - ys + z . + cs . the 5th power of a3 + Ans . 8a " . Ans . 16a x * . Ans . —512 x®y® . ' ( 50 ...
Page 21
... square , a2 is the first , and 6 is the last terna : in the cube , a is the first , and the last , & c . 2. That in the intermediate terms , the powers of a decrease , while the powers of b increase , by unity , in each successive term ...
... square , a2 is the first , and 6 is the last terna : in the cube , a is the first , and the last , & c . 2. That in the intermediate terms , the powers of a decrease , while the powers of b increase , by unity , in each successive term ...
Page 24
... square a + b + c ; placing a vinculum over a + b , and viewing it as one quantity , we shall have ( a + b + c ) ... square root of is 462 26 26 26 461 From these data , we discover that the square , cube , & c . roots of simple and ...
... square a + b + c ; placing a vinculum over a + b , and viewing it as one quantity , we shall have ( a + b + c ) ... square root of is 462 26 26 26 461 From these data , we discover that the square , cube , & c . roots of simple and ...
Page 25
... square root of a2 is either + a , or — a ; for ( + a ) X ( + a ) = + a3 , and ( — a ) × ( — a ) = + a2 . ( Ilins ... square root of gr2 . Here / 9r2 = 3x = 3.x. 2. The cube root of 88r = 2x = 2.x. 3. Required the square root of 4 ...
... square root of a2 is either + a , or — a ; for ( + a ) X ( + a ) = + a3 , and ( — a ) × ( — a ) = + a2 . ( Ilins ... square root of gr2 . Here / 9r2 = 3x = 3.x. 2. The cube root of 88r = 2x = 2.x. 3. Required the square root of 4 ...
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Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 209 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Page 284 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.
Page 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...
Page 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.