A Course of Mathematics: For the Use of Academies, as Well as Private Tuition, Volume 2S. Cambell, 1818 - 558 pages |
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Page 25
... determine the other angles , without first finding any of the sides ? Ex . 17. The sides of a triangle are to each other as the fractions ,, : what are the angles ? Ex . 18. Show that the secant of 60 ° , is double the tan- gent of 45 ...
... determine the other angles , without first finding any of the sides ? Ex . 17. The sides of a triangle are to each other as the fractions ,, : what are the angles ? Ex . 18. Show that the secant of 60 ° , is double the tan- gent of 45 ...
Page 26
... determine the third ; while in the latter they never do . 2dly . The surface of a plane triangle cannot be determined from a knowledge of the angles alone ; while that of a spherical triangle always can . 5. The sides of a spherical ...
... determine the third ; while in the latter they never do . 2dly . The surface of a plane triangle cannot be determined from a knowledge of the angles alone ; while that of a spherical triangle always can . 5. The sides of a spherical ...
Page 27
... determine it form a kind of triangular pyramid , BCGA of which the vertex G is at the centre of the sphere , the base ABC a portion of the spherical surface , and the faces AGC . AGB , BGC , sectors of the great circles whose ...
... determine it form a kind of triangular pyramid , BCGA of which the vertex G is at the centre of the sphere , the base ABC a portion of the spherical surface , and the faces AGC . AGB , BGC , sectors of the great circles whose ...
Page 35
... determine the angles . And hence all those ge- ometers , from the time of Euclid down to the present period , who have confined their attention principally to the magnitude of the plane angles instead of their relative positions , have ...
... determine the angles . And hence all those ge- ometers , from the time of Euclid down to the present period , who have confined their attention principally to the magnitude of the plane angles instead of their relative positions , have ...
Page 58
... Determine the solid angles of a regular pyramid , with hexagonal base , the altitude of the pyramid being to each side of the base as 2 to 1 . Ans . Plane angle between each two lateral faces 126 ° 52′11 ′′ . between the base and each ...
... Determine the solid angles of a regular pyramid , with hexagonal base , the altitude of the pyramid being to each side of the base as 2 to 1 . Ans . Plane angle between each two lateral faces 126 ° 52′11 ′′ . between the base and each ...
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Common terms and phrases
absciss altitude axis ball base beam becomes body centre of gravity circle circumference consequently Corol cosine curve denote density descending determine diameter direction distance earth elevation equa equal equation equilibrio EXAM expression feet find the fluent fluid fluxion force given Hence horizontal hyperbola inches inclined plane length lever logarithm measured meridian motion move nearly oblique parabola parallel pendulum perp perpendicular polygon pressure prob PROBLEM projectile prop proportional PROPOSITION quadrant quantity radius ratio resistance right angles right line roots Scholium sides sin² sine solid angle space specific gravity spherical angle spherical excess spherical triangle spherical trigonometry square supposed surface tangent theorem theref three angles tion trapezium velocity vibrations weight whence whole
Popular passages
Page 15 - 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 206 - Then say, As the weight lost in water, Is to the whole weight, So is the specific gravity of water, To the specific gravity of the body.
Page 407 - Or, by art. 31* of the same, the pressure is equal to the weight of a column of the fluid, whose base is equal to the surface pressed, and its altitude equal to the depth of the centre of gravity below...
Page 173 - 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 421 - From the same table it also appears, that the time of the ball's flight is nearly as the range ; the gun and elevation being the same.
Page 421 - ... increasing the charge, the velocity gradually diminishes, till the bore is quite full of powder. That this charge for the greatest velocity is greater as the gun is longer, but yet not greater in so high a proportion as the length of the gun is ; so that the part of the bore filled with powder, bears a less proportion to the whole bore in the long guns, than it does in the shorter ones ; the part which is filled being indeed nearly in the inverse ratio of the square root of the empty part.
Page 175 - 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 417 - Finally, as these experiments prove the regulations with respect to the weight of powder and shot, when discharged from the same piece of ordnance ; so, by making similar experiments with a gun varied in its length by cutting off from it a certain part, before each set of trials, the effects and general rules for the different lengths of guns, may be with certainty determined by them.
Page 107 - ... powder, and that but a small one too ; so that all those nearly agree with the parabolic theory. Other experiments have also been carried on with the ballistic pendulum, at different times ; from which have been obtained some of the, laws for the quantity of powder, the weight and velocity of the ball, the length of the gun, &c. Namely, that the velocity of the ball varies as the square root of the charge directly, and as the square root of the weight of ball reciprocally ; and 'that, some rounds...