A Course of Mathematics ...: Composed for the Use of the Royal Military Academy ...F. C. and J. Rivington, 1811 - Mathematics |
From inside the book
Results 1-5 of 17
Page 169
... vibrating like a pen- dulum : Also , the velocities will be equal , at all equal alti- tudes ; and the ascent and descent will be performed in the same time , if the curves be the same . PROPOSITION XXIX . 142. The Times in which Bodies ...
... vibrating like a pen- dulum : Also , the velocities will be equal , at all equal alti- tudes ; and the ascent and descent will be performed in the same time , if the curves be the same . PROPOSITION XXIX . 142. The Times in which Bodies ...
Page 170
... vibrating like a pendulum , the lengths being DC , DC ; therefore the times of the vibration of pendulums , in similar arcs of any curves , are as the square roots of the lengths of the pendulums . SCHOLIUM . 145. Having , in the last ...
... vibrating like a pendulum , the lengths being DC , DC ; therefore the times of the vibration of pendulums , in similar arcs of any curves , are as the square roots of the lengths of the pendulums . SCHOLIUM . 145. Having , in the last ...
Page 171
... Vibration , is to the Time in which a Body falls through Half the Length of the Pendulum , as the Circumference of a ... vibrating , describe the arc FBf . Divide FB into in- numerable small parts , one of which is Gg ; draw FEL , GM ...
... Vibration , is to the Time in which a Body falls through Half the Length of the Pendulum , as the Circumference of a ... vibrating , describe the arc FBf . Divide FB into in- numerable small parts , one of which is Gg ; draw FEL , GM ...
Page 172
... vibration , is to the time of falling through half CB , as the circumference of any circle , is to its diameter . 149. Coral . 149. Carol . 1. Hence all the vibrations of a 172 OF MOTION , FORCES , & c .
... vibration , is to the time of falling through half CB , as the circumference of any circle , is to its diameter . 149. Coral . 149. Carol . 1. Hence all the vibrations of a 172 OF MOTION , FORCES , & c .
Page 173
... vibration of the pendulum . 150. And if the pendulum vibrate in a small arc of a circle ; because that small arc nearly coincides with the small cy- cloidal arc at the vertex B ; therefore the time of vibration in the small arc of a ...
... vibration of the pendulum . 150. And if the pendulum vibrate in a small arc of a circle ; because that small arc nearly coincides with the small cy- cloidal arc at the vertex B ; therefore the time of vibration in the small arc of a ...
Other editions - View all
A Course of Mathematics ...: Composed for the Use of the Royal Military Academy Charles Hutton,Olinthus Gregory No preview available - 2016 |
Common terms and phrases
absciss altitude angle avoirdupois axis ball base body bottom breadth CA² CD² centre of gravity circle circumference column common logarithm cone consequently constant Corol cosine cube cubic cubic foot curvature curve cycloid cylinder DE² denote density descending diameter direction distance divided draw drawn earth ellipse equal equation figure find the area find the fluent fluent of EXAM fluid foot force frustum given fluxion Hence hyperbola inches inclined plane length logarithm measure motion moving multiply nearly ordinate parabola parallel parallelogram pendulum perpendicular pressure PROBLEM proportion PROPOSITION QUEST quicksilver radius radius of curvature ratio rectangle resistance SCHOLIUM secant side sine solid space specific gravity square supposing surface tangent theor THEOREM theref thickness triangle velocity vibration weight whole yards
Popular passages
Page 64 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 1 - Geom.) is an arc of any circle contained between the two lines which form that angle, the angular point being the centre ; and it is •estimated by the number of degrees contained in that arc.
Page 171 - Half the Length of the Pendulum, as the Circumference of a Circle is to its Diameter...
Page 227 - Hence the magnitude of the whole body, is to the magnitude of the part immersed, as the specific gravity of the fluid, is to that of the body.
Page 13 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Page 88 - GLAZIERS' WORK. — Glaziers take their dimensions either in feet, inches, and parts ; or feet, tenths, and hundredths. And they compute their work in square feet. In taking the length and breadth of a window, the cross bars between the squares are included. Also, windows of round or oval forms are measured as square, measuring them to their greatest length and breadth, on account of the waste in cutting the glass.
Page 44 - Ex. 2. To find the whole surface of a triangular prism, whose length is 20 feet, and each side of its end or base 18 inches.
Page 11 - DF; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference.
Page 22 - A ladder 40 feet long may be so placed that it shall reach a window 33 feet from the ground on one side of the street, and by turning it over, without moving the foot out of its place, it will do the same by a window 21 feet high on the other side. Required the breadth of the street.
Page 87 - Required the quantity of plastering in a room, the length being 14 feet 5 inches, breadth 13 feet 2 inches, and height 9 feet 3 inches to the under side of the cornice, which girts...