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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Σελίδα 77
... 3 . In an inverted parabola the time of descending down any chord from a point in the curve to the vertex , is equal to the time of falling freely to a horizontal line which is at a distance below the vertex equal to DYNAMICS . 77.
... 3 . In an inverted parabola the time of descending down any chord from a point in the curve to the vertex , is equal to the time of falling freely to a horizontal line which is at a distance below the vertex equal to DYNAMICS . 77.
Σελίδα 79
... parabola upon the plane . 4. Determine the angle of projection for which the horizontal range will be greatest , the velocity of projection being given . 5. If the velocity of projection be given , determine DYNAMICS . 79.
... parabola upon the plane . 4. Determine the angle of projection for which the horizontal range will be greatest , the velocity of projection being given . 5. If the velocity of projection be given , determine DYNAMICS . 79.
Σελίδα 80
... parabola described . 7. The latus rectum of the path of a projectile is a , and the horizontal range b , determine the velocity and di- rection of projection . 8 . Determine the angle of projection so that the hori- zontal range and the ...
... parabola described . 7. The latus rectum of the path of a projectile is a , and the horizontal range b , determine the velocity and di- rection of projection . 8 . Determine the angle of projection so that the hori- zontal range and the ...
Σελίδα 81
... parabola described by the body after leaving the plane . 17. Find the velocity and direction of projection of a ball , that it may be 100 feet above the earth at one mile distance , and may strike the ground at a distance of three miles ...
... parabola described by the body after leaving the plane . 17. Find the velocity and direction of projection of a ball , that it may be 100 feet above the earth at one mile distance , and may strike the ground at a distance of three miles ...
Σελίδα 82
... parabola , the axis of which is vertical , and is reflected at the curve ; determine the latus rectum of the parabola described . The position of a ball on a triangular billiard table being given ; it is required to shew that there are ...
... parabola , the axis of which is vertical , and is reflected at the curve ; determine the latus rectum of the parabola described . The position of a ball on a triangular billiard table being given ; it is required to shew that there are ...
Άλλες εκδόσεις - Προβολή όλων
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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.