A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Band 2W. E. Dean, 1831 |
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Seite 35
... Solid angle is defined by Euclid , that which is made by the meeting of more than two plane angles , which are not ... angle . According to this definition , solid angles bear just the same relation to the surfaces which comprise them ...
... Solid angle is defined by Euclid , that which is made by the meeting of more than two plane angles , which are not ... angle . According to this definition , solid angles bear just the same relation to the surfaces which comprise them ...
Seite 35
... angle BCA , and that DF is equal the supplement to GK , the measure of the angle ABC which constitutes the first part of the proposi- tion . ABC . 2dly . The respective measures of the angles of the triangle DEF are supplemental to the ...
... angle BCA , and that DF is equal the supplement to GK , the measure of the angle ABC which constitutes the first part of the proposi- tion . ABC . 2dly . The respective measures of the angles of the triangle DEF are supplemental to the ...
Seite 37
... angles of any spheric polygon , is always less than 2n right angles , but greater than ( 2n - 4 ) right angles , n denoting the num ber of angles of the polygon . GENERAL SCHOLIUM . On the Nature and Measure of Solid Angles . A Solid angle ...
... angles of any spheric polygon , is always less than 2n right angles , but greater than ( 2n - 4 ) right angles , n denoting the num ber of angles of the polygon . GENERAL SCHOLIUM . On the Nature and Measure of Solid Angles . A Solid angle ...
Seite 38
... solid angle made by the planes at their common point of meeting : for no change can be conceived in the relative position of those planes , that is , in the magni- tude of the solid angle , without a corresponding and propor tional ...
... solid angle made by the planes at their common point of meeting : for no change can be conceived in the relative position of those planes , that is , in the magni- tude of the solid angle , without a corresponding and propor tional ...
Seite 39
... solid angles formed by n bounding planes , by the excess of the sum of the angles of inclination of the several ... angle of 180 ° . The maximum limit of solid angles is measured by the surface of a hemisphere , in like manner as the ...
... solid angles formed by n bounding planes , by the excess of the sum of the angles of inclination of the several ... angle of 180 ° . The maximum limit of solid angles is measured by the surface of a hemisphere , in like manner as the ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
abscissas altitude axis ball base beam becomes body centre of gravity chords circle consequently Corol cosine curve denote density descending determine diameter direction distance draw earth equa equal equation equilibrio EXAM expression feet find the fluent fluid fluxion force given plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion multiplied nearly ordinates parabola parallel pendulum perpendicular 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 velocity vertex vertical plane vertical projections vibrations weight whole
Beliebte Passagen
Seite 459 - Or, by an. 249 of the same, the pressure is equal to the weight of a column of the fluid...
Seite 66 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Seite 195 - VI, its Corollaries and Scholium, for Constant Forces, are true in the Motions of. Bodies freely descending by their own Gravity ; namely, that the Velocities are as the Times, and the Spaces as the Squares of the Times, or as the Squares of the Velocities. FOR, since the force of gravity is uniform, and constantly the same, at all places near the earth's surface, or at nearly the same distance from the centre of the earth ; and since • this is the force by which bodies descend to the surface ;...
Seite 239 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Seite 289 - The workmen thought that substituting part silver was only a proper <perquisite; which taking air, Archimedes was appointed to examine it ; who, on putting...
Seite 35 - 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.
Seite 75 - Let a, b, c, be the sides, and A, B, c, the angles of a spherical triangle, on the surface of a sphere whose radius is r ; then...
Seite 385 - Multiply the number in the table of multiplicands, by the breadth and square of the depth, both in inches, and divide that product by the length, also, in inches; the quotient will be the weight in Jbs.t Example 1.
Seite 244 - 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...
Seite 140 - Body is either Hard, Soft, or Elastic. A Hard Body is that whose parts do not yield to any stroke or percussion, but retains its figure unaltered. A Soft Body is that whose parts yield^to any stroke or impression, without restoring themselves again ; the figure of the body remaining altered.