A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Band 2W. E. Dean, 1831 |
Im Buch
Ergebnisse 1-5 von 100
Seite 5
... Hence we may inmediately deduce a very important theo- rem : for , the first of these equations , divided by the second , = , and the first divided by the third gives inc gives sin . A su . B = sin . A C ; whence since two equal ...
... Hence we may inmediately deduce a very important theo- rem : for , the first of these equations , divided by the second , = , and the first divided by the third gives inc gives sin . A su . B = sin . A C ; whence since two equal ...
Seite 20
... Hence , substituting I for R and 3 for cos a , in the ex- pression sin a ± √ √ ( 2R2 + 2R cos A ) ... ( equa . XII ) , it becomes sin 15 ° = √ ( 2 − √ / 3 ) 2588190 . Hence , sin 75 ° cos15 ° ✓ [ 1- ( 2 − √ / 3 ) ] = { √ ( 2 + ...
... Hence , substituting I for R and 3 for cos a , in the ex- pression sin a ± √ √ ( 2R2 + 2R cos A ) ... ( equa . XII ) , it becomes sin 15 ° = √ ( 2 − √ / 3 ) 2588190 . Hence , sin 75 ° cos15 ° ✓ [ 1- ( 2 − √ / 3 ) ] = { √ ( 2 + ...
Seite 23
... Hence the process is this : From tan A + tan B + tan c = 5.3047057 Take tan A + tan B. Remains tan c = : 3.1601988 • · = 2 · 1445069 = tan 65 ° . From tan A + tan B + tan c = 5 · 3047057 Take tan B + tan c . Remains tan a . 3.8765577 ...
... Hence the process is this : From tan A + tan B + tan c = 5.3047057 Take tan A + tan B. Remains tan c = : 3.1601988 • · = 2 · 1445069 = tan 65 ° . From tan A + tan B + tan c = 5 · 3047057 Take tan B + tan c . Remains tan a . 3.8765577 ...
Seite 27
... Hence it follows , that the surface of a spherical triangle BAC , and the three planes which determine it , form a kind of triangular pyramid , BCGA , of which the vertex & is at the centre of the sphere , the base ABC a portion of the ...
... Hence it follows , that the surface of a spherical triangle BAC , and the three planes which determine it , form a kind of triangular pyramid , BCGA , of which the vertex & is at the centre of the sphere , the base ABC a portion of the ...
Seite 35
... Hence the excess of the three angles of any sphe- rical triangle above two right angles , termed technically the spherical excess , furnishes a correct measure of the surface of that triangle . Cor . 2. If = 3.141593 , and d the ...
... Hence the excess of the three angles of any sphe- rical triangle above two right angles , termed technically the spherical excess , furnishes a correct measure of the surface of that triangle . Cor . 2. If = 3.141593 , and d 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.