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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 113
... ellipse or hyperbola are conjugate . Prove that all parallelograms whose sides touch an ellipse at the ends of conjugate diameters are equal . Prove that such parallelograms have the least area of all which circumscribe the ellipse . 14 ...
... ellipse or hyperbola are conjugate . Prove that all parallelograms whose sides touch an ellipse at the ends of conjugate diameters are equal . Prove that such parallelograms have the least area of all which circumscribe the ellipse . 14 ...
Σελίδα 115
... ellipse varies as either axis when the other is constant , and that the area of a circle of radius unity 3.14 ... , find the area of the = ellipse whose axes are 3 and 5 . 11. Find the sum to n terms of a geometric series . What is ...
... ellipse varies as either axis when the other is constant , and that the area of a circle of radius unity 3.14 ... , find the area of the = ellipse whose axes are 3 and 5 . 11. Find the sum to n terms of a geometric series . What is ...
Σελίδα 123
... ellipse ; required the law of force tending to the centre . Give the reasoning by which Newton extends the result obtained to the case of a parabola , or an hyperbola . Is the same kind of reasoning applicable when the centre of force ...
... ellipse ; required the law of force tending to the centre . Give the reasoning by which Newton extends the result obtained to the case of a parabola , or an hyperbola . Is the same kind of reasoning applicable when the centre of force ...
Σελίδα 125
... ellipse , and the positions of one focus and of one point in the curve , give a geometrical construction for finding the centre . 10. P is any point in an ellipse , AA SENATE - HOUSE PROBLEMS . 125.
... ellipse , and the positions of one focus and of one point in the curve , give a geometrical construction for finding the centre . 10. P is any point in an ellipse , AA SENATE - HOUSE PROBLEMS . 125.
Σελίδα 126
... ellipse , AA ' its axis major , NP an ordinate to the point P ; to any point Q in the curve draw AQ , A'Q meeting NP in R and S ; shew that NR . NS NP2 . = 11. PSP is a focal chord of a parabola , RDr the directrix , meeting the axis in ...
... ellipse , AA ' its axis major , NP an ordinate to the point P ; to any point Q in the curve draw AQ , A'Q meeting NP in R and S ; shew that NR . NS NP2 . = 11. PSP is a focal chord of a parabola , RDr the directrix , meeting the axis in ...
Άλλες εκδόσεις - Προβολή όλων
A Collection of Problems and Examples, Adapted to the Elementary Course of ... Harvey Goodwin Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
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A Collection of Problems and Examples, Adapted to the 'Elementary Course of ... Harvey Goodwin Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2010 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 111 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 160 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 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.
Σελίδα 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.