A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well as Private Tuition, Volume 2Samuel Campbell, Evert Duyckinck, T. & J. Swords, 1816 - Mathematics |
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Page 151
... cycloidal arc_AC = double the chord AD ; The semi - cycloid ACA = double the diameter AB , and The tangent CF is parallel to the chord AD . PROPOSITION XXX . 148. When a Pendulum vibrates in a cycloid ; the Time of one Vibration , is to ...
... cycloidal arc_AC = double the chord AD ; The semi - cycloid ACA = double the diameter AB , and The tangent CF is parallel to the chord AD . PROPOSITION XXX . 148. When a Pendulum vibrates in a cycloid ; the Time of one Vibration , is to ...
Page 152
... cycloid , His equal to Gg . If another body descend down the chord EB , it will have the same velocity as the ball in the cycloid has at the same height . So that Kk and Gg are passed over with the same velocity , and consequently the ...
... cycloid , His equal to Gg . If another body descend down the chord EB , it will have the same velocity as the ball in the cycloid has at the same height . So that Kk and Gg are passed over with the same velocity , and consequently the ...
Page 153
... cycloid whether great or small , are performed in the same time , which time is to the time of falling through the ... cycloidal arc ; consequently the time of vibration * in a small circular , arc is equal to where / is the radius 28 of ...
... cycloid whether great or small , are performed in the same time , which time is to the time of falling through the ... cycloidal arc ; consequently the time of vibration * in a small circular , arc is equal to where / is the radius 28 of ...
Page 370
... cycloid . Ans . r = 24 / aa - ax , where x is the absciss , and a the diameter of the generating circle . OF INVOLUTE AND EVOLUTE CURVES . 11. AN Evolute is any curve supposed to be evolved or opened , which having a thread wrapped ...
... cycloid . Ans . r = 24 / aa - ax , where x is the absciss , and a the diameter of the generating circle . OF INVOLUTE AND EVOLUTE CURVES . 11. AN Evolute is any curve supposed to be evolved or opened , which having a thread wrapped ...
Page 373
... cycloid , equal to the former . TO FIND THE CENTRE OF GRAVITY , 17. By referring to prop . 42 , & c . in Mechanics , it is seen what are the principles and nature of the Centre of Gravity in any figure , and how it is generally ...
... cycloid , equal to the former . TO FIND THE CENTRE OF GRAVITY , 17. By referring to prop . 42 , & c . in Mechanics , it is seen what are the principles and nature of the Centre of Gravity in any figure , and how it is generally ...
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Common terms and phrases
absciss altitude axis ball base beam becomes body centre of gravity circle column consequently Corol cosine cubic curve cycloid cylinder denote density descending determine diameter direction distance earth equa equal equation equilibrio EXAM expression feet find the fluent fluid force given fluxion gives greatest Hence horizontal hyperbola inches inclined plane length lever logarithm measured motion moving nearly oblique ordinate parabola parallel pendulum perpendicular plane pressure prob PROBLEM projectile prop proportion PROPOSITION quantity radius ratio rectangle resistance right angles right line roots Scholium sides sin² sine solid angle space specific gravity spherical excess spherical triangle square supposed surface tangent theorem theref tion trapezium variable velocity vertical vibrations weight whole
Popular passages
Page 437 - Or, by art. 314 of the same, .the pressure is equal to the weight of a column of the fluid...
Page 258 - ... and — . The preceding equation is only of the fourth power or degree ; but it is manifest that the above remark applies to equations of higher or lower dimensions : viz, that in general . an equation of any degree whatever has as many roots as there are units in the exponent of the highest power of the unknown quantity, and that each root has the property of rendering, by its substitution in place of the unknown quantity, the aggregate' of all the terms of the equation equal to nothing.
Page 34 - Two planes are said to have the same or a like inclination to one another which two other planes have, when the said angles of inclination are equal to one another.
Page 249 - Vespasian weighed, suppose 10,000 pounds; and was moved, let us admit, with such such a velocity, by strength of hand, as to pass through 20 feet in one second of time ; and this was found sufficient to demolish the walls of Jerusalem. The question is, with what velocity a 32lb ball must move, to do the same execution ? Ans.
Page 209 - As the weight lost in water is to the whole, or absolute weight ; so is the specific gravity of water ' " to "the specific gravity 'of the body . 2.
Page 241 - ... as the greatest product is to the whole weight of the compound, so is each of the other products to the weights of the two ingredients.
Page 31 - ... the triangle DEF, three others might be formed by the intersection of the three arcs DE, EF, DF. But the proposition immediately before us is applicable only to the central triangle, which is distinguished from the other three by the circumstance (see the last figure) that the two angles A and D lie on the same side of BC, the...
Page 167 - The screw is a spiral thread or groove cut round a cylinder, and every where making the same angle with the length of it. So that if the surface of the cylinder, with this spiral thread on it, were unfolded and stretched into a plane, the spiral thread would form a straight inclined plane, whose length would be to its height, as the circumference of the cylinder...
Page 450 - From a general inspection of this second course of these experiments, it appears that all the deductions and observations made on the former course, are here corroborated and strengthened, respecting the velocities and weights of the, balls, and charges of powder, &c. It furt-her appears also that the velocity of the ball increases with the increase of - charge Penetratio>^ of Balls into solid Eln^wpod.
Page 255 - ... ounces, he found by calculation what part of the king's gold had been changed. And you are desired to repeat the process. Ans.