A Collection of Problems and Examples Adapted to the "Elementary Course of Mathematics.": With an Appendix Containing the Questions Proposed During the First Three Days of the Senate-House Examinations in the Years 1848, 1849, 1850, and 1851J. Deighton, 1851 - 173 sider |
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Side 28
... quantities remaining are in the proportion of 8 : 3 . After they become half empty , he puts 10 gallons of water into each , and the quantities of liquor now in them are as How many gallons will each hold ? 9 : 5 . Ans . They will hold ...
... quantities remaining are in the proportion of 8 : 3 . After they become half empty , he puts 10 gallons of water into each , and the quantities of liquor now in them are as How many gallons will each hold ? 9 : 5 . Ans . They will hold ...
Side 30
... quantities of silver as before in each mixture double the former quantities of gold had been added , the values of two coins of equal weights would have been to each other as 7 : 11. Deter- mine the proportion of gold to silver in each ...
... quantities of silver as before in each mixture double the former quantities of gold had been added , the values of two coins of equal weights would have been to each other as 7 : 11. Deter- mine the proportion of gold to silver in each ...
Side 34
... arithmetical mean between a and b is greater than the geometrical . 6. If quantities are in geometrical progression , their differences are in geometrical progression . 7 . There are three numbers in geometrical progres- sion 34 ALGEBRA .
... arithmetical mean between a and b is greater than the geometrical . 6. If quantities are in geometrical progression , their differences are in geometrical progression . 7 . There are three numbers in geometrical progres- sion 34 ALGEBRA .
Side 35
... quantities in geometrical progression , and the sum of their reciprocals ; find the quantities themselves . 11. In every geometrical progression consisting of an odd number of terms , the sum of the squares of the terms is equal to the ...
... quantities in geometrical progression , and the sum of their reciprocals ; find the quantities themselves . 11. In every geometrical progression consisting of an odd number of terms , the sum of the squares of the terms is equal to the ...
Side 39
... quantities ; ( 1 + } ) 1o , ( 1 − 1 ) 2 , ( 2 − 3 ) −1o . 10. If N = the nth term of ( 1 - x ) " , then the series after the first n terms m m m + + & c . - Na ( 1 - + 1 ) + No ( 1-1 ) ( 1-1 ) . n n + 11 . If 2 + +1 = 0 , then will n ...
... quantities ; ( 1 + } ) 1o , ( 1 − 1 ) 2 , ( 2 − 3 ) −1o . 10. If N = the nth term of ( 1 - x ) " , then the series after the first n terms m m m + + & c . - Na ( 1 - + 1 ) + No ( 1-1 ) ( 1-1 ) . n n + 11 . If 2 + +1 = 0 , then will n ...
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Almindelige termer og sætninger
angular points arithmetical arithmetical mean arithmetical series axis base bisects centre of gravity chord circle concave convex lens cos² cosec curve cylinder Describe determine diameter direction distance Divide drawn elastic balls ellipse equal equation equilibrium feet find the height Find the number find the position Find the velocity fluid focal length force geometrical focus geometrical progression geometrical series given point given velocity given weight horizontal plane hyperbola immersed inches incident inclined plane inscribed latus rectum luminous point mirror motion moving Multiply observed parabola parallel parallelogram pencil of rays perpendicular placed pressure proportional prove pullies quantities radii radius ratio reflexion refracted respectively right angle shew sides sin² specific gravity sphere spherical square St John's College straight line string passing Subtract surface tangent tower triangle vertex
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Side 111 - If two triangles have two sides of the one equal to two sides of the...
Side 128 - To divide a given straight line 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.
Side 111 - 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.
Side 112 - EQUAL straight lines in a circle are equally distant from the centre ; and those which are equally distant from the centre, are equal to one another.
Side 144 - ... a circle. The angle in a semicircle is a right angle: the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Side 160 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Side 112 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 160 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.