## New series of The mathematical repository, Volume 4 |

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Afternoon.—Mr altitude attraction axis base body centre of gravity chord circular arc circumference cone conic section consequently construction cosine cube Cunliffe curve cycloid denote described determine diameter difference distance draw drawn ellipse equal equation expression Find the fluents fluid fluxion formula given circle given point given ratio hence horizontal hyperbola inscribed intersection John Pond latitude Lemma length logarithmic Mathematical meet method orbit ordinate Palaba parabola parallel pendulum perpendicular plane triangle position prime numbers Prop Proposer Prove quadrant quantities QUESTION radius rectangle right angles right ascension roots Royal Military Academy segments shew sides similar triangles sin3 sin5 sine solid Solution specific gravity sphere spherical spherical reflector spheroid square straight line subtangent supposed surface tangent theorem tion velocity vertex vibrates seconds whence wherefore

### Popular passages

Page 34 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.

Page 34 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Page 51 - If the radii, of the tube, and of the basin, of a barometer, be 1 and 3 ; and the index shews, at sight, the height of the mercury in the tube, above that in the basin ; prove that the inch upon the scale : a real inch :: 8 : 9, the thickness of the tube being neglected.

Page 27 - Shew that the sum of the products of each body into the square of its velocity is a minimum, when the velocities are reciprocally proportional to the quantities of matter in the bodies.

Page 160 - If the circumference of a circle be divided into any number of equal parts, the chords joining the successive points of division form a regular polygon inscribed in the circle ; and the tangents drawn at the points of division form a regular polygon circumscribed about the circle.

Page 39 - If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides.

Page 17 - ... 8. If a square be inscribed in a circle and another circumscribed about both : compare the pressures upon the circle and the squares when immersed vertically in a fluid ; the angular point of the circumscribing square coinciding with the surface of the fluid. 9. A hollow cone, whose vertical angle is 60°, is filled with water, and placed with its base downwards. It is required to determine the place where a small orifice must be made in its side, so that the issuing fluid may strike the horizontal...

Page 68 - To find the form of equilibrium of an arch built from one planet to another, conceiving each particle animated with a force directed towards the Sun and varying inversely as the square of the distance from its centre...

Page 124 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.

Page 74 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included...