A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 |
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Page 114
... straight lines , and in strict . ness no part of a curve is a right line , some geometers prefer defining curves otherwise : thus , in a straight line , to be called the line of the abscissas , from a certain point let a line arbi ...
... straight lines , and in strict . ness no part of a curve is a right line , some geometers prefer defining curves otherwise : thus , in a straight line , to be called the line of the abscissas , from a certain point let a line arbi ...
Page 585
... straight line PQ imagine two straight lines Pr and Qa ' to be drawn at right angles tothe hori . zontal plane ABCD and meeting it in r ' and q ' ; and from the same points r and a two other straight lines PP " and QQ " to be drawn at ...
... straight line PQ imagine two straight lines Pr and Qa ' to be drawn at right angles tothe hori . zontal plane ABCD and meeting it in r ' and q ' ; and from the same points r and a two other straight lines PP " and QQ " to be drawn at ...
Page 586
... line in PQ will meet the horizontal plane in the straight line r'q ' ; the straight line r'q ' is therefore called the hori- zontal projection of the straight line PQ . From this construc- tion it is plain that the projection of a straight ...
... line in PQ will meet the horizontal plane in the straight line r'q ' ; the straight line r'q ' is therefore called the hori- zontal projection of the straight line PQ . From this construc- tion it is plain that the projection of a straight ...
Page 587
... straight line pa is said to be given in space when its projections P'Q ' and r " q " are given ; and a straight line rQ is said to be found when its projections ro ' , P " Q " are found . To which we may add that the two planes passing ...
... straight line pa is said to be given in space when its projections P'Q ' and r " q " are given ; and a straight line rQ is said to be found when its projections ro ' , P " Q " are found . To which we may add that the two planes passing ...
Page 588
... straight line be given by its projections , it is required to find its height above the horizontal plane at any point of its projection on that plane . D Let ABCD be the hori . zontal plane , and EFCD the vertical plane , which by ...
... straight line be given by its projections , it is required to find its height above the horizontal plane at any point of its projection on that plane . D Let ABCD be the hori . zontal plane , and EFCD the vertical plane , which by ...
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Common terms and phrases
absciss altitude axis ball base beam becomes body centre of gravity circle conic surface consequently Corol cosine curve denote density descending determine diameter direction distance draw earth equa equal equation equilibrio EXAM expression feet find the fluent fluid force given plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion moving multiplied nearly ordinate parabola parallel pendulum perpendicular position pressure prob PROBLEM PROP proportional quantity radius ratio rectangle resistance right angles right line roots Scholium side sine solid angle space specific gravity spherical angle spherical excess spherical triangle square straight line supposed surface tangent theorem theref tion variable velocity vertex vertical plane vertical projections vibrations weight whole
Popular passages
Page 13 - 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.
Page 469 - Or, by art. 249 of the same, the pressure is equal to the weight of a column of the fluid...
Page 74 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Page 299 - The workmen thought that substituting part silver was only a proper <perquisite; which taking air, Archimedes was appointed to examine it ; who, on putting...
Page 158 - MECHANICAL POWERS are certain simple instruments employed in raising greater weights, or overcoming greater resistance than could be effected by the direct application of natural strength. They are usually accounted six in number; viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw.
Page 249 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 301 - In the doctrine of fluxions, magnitudes or quantities of all kinds are considered as not made up of a number of small parts, but as generated by continued motion, by means of which they increase or decrease ; as a line by the motion of a point ; a surface by the motion of a line ; and a solid by the motion of a surface.
Page 254 - Weigh the denser body and the compound mass, separately, both in water, and out of it ; then find how much each loses in water, by subtracting its weight in water from its weight in air; and subtract the less of these remainders from the greater. Then...
Page 494 - The reason is, all bodies lose some of their weight in a fluid, and the weight which a body loses in a fluid, is to its whole weight, as the specific gravity of the fluid is to that of the body.
Page 461 - ... horizontal *. 2. The theorems just given may serve to show, in what points of view machines ought to be considered by those who would labour beneficially for their improvement. The first object of the utility of machines consists in furnishing the means of giving to the moving force the most commodious direction ; and, when it can be done, of causing its action to be applied immediately to the body to be moved. These can rarely be united : but the former can be accomplished in most instances...