A Course of Mathematics for the Use of Academies: As Well as Private Tuition, Volume 2S. Campbell, 1826 - Geometry |
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Page 20
... base , that perpendicular will be the sine of 60 ° , and the half base the sine of 30 ° , the side of the triangle being the assumed radius . Thus , if it be R , we shall have R for the sine of 30 ° , and √ R2 — 1R2 = { R√3 , for the ...
... base , that perpendicular will be the sine of 60 ° , and the half base the sine of 30 ° , the side of the triangle being the assumed radius . Thus , if it be R , we shall have R for the sine of 30 ° , and √ R2 — 1R2 = { R√3 , for the ...
Page 24
... base is to the difference of the other two sides , as the sine of half the sum of the angles at the base , to the sine of half their differ- ence : also , that the base is to the sum of the other two sides as as the cosine of half the ...
... base is to the difference of the other two sides , as the sine of half the sum of the angles at the base , to the sine of half their differ- ence : also , that the base is to the sum of the other two sides as as the cosine of half the ...
Page 25
... base , to the cosine of half their difference . Ex . 14. How must three trees , A , B , C , be planted , so that the angle at A may be double the angle at B , the angle at в dou- ble that at c ; and so that a line of 400 yards may just ...
... base , to the cosine of half their difference . Ex . 14. How must three trees , A , B , C , be planted , so that the angle at A may be double the angle at B , the angle at в dou- ble that at c ; and so that a line of 400 yards may just ...
Page 27
... base ABC a portion of the spherical surface , and the faces AGC , AGB , BGC , sectors of the great circles whose intersections determine the sides of the triangle . B M P P Def . 6. A line perpendicular to the plane of a great circle ...
... base ABC a portion of the spherical surface , and the faces AGC , AGB , BGC , sectors of the great circles whose intersections determine the sides of the triangle . B M P P Def . 6. A line perpendicular to the plane of a great circle ...
Page 29
... bases . might also be shown , that a spherical triangle is equilateral , isosceles , or scalene , according as it hath three equal , two equal , or three unequal angles : and again , that the greatest side is always opposite to the ...
... bases . might also be shown , that a spherical triangle is equilateral , isosceles , or scalene , according as it hath three equal , two equal , or three unequal angles : and again , that the greatest side is always opposite to the ...
Other editions - View all
A Course of Mathematics, Vol. 2 of 2: For the Use of Academies, as Well as ... Charles Hutton No preview available - 2018 |
A Course of Mathematics, Vol. 2 Of 2: For the Use of Academies As Well As ... Charles Hutton No preview available - 2018 |
A Course of Mathematics, Vol. 2 of 2: For the Use of Academies, as Well as ... Charles Hutton No preview available - 2018 |
Common terms and phrases
abscissas altitude axis ball base beam body centre of gravity circle co-efficient conic surface consequently Corol cosine curve denote density descending determine diameter direction distance draw elevation equa equal equation equilibrio EXAM expression feet find the fluent fluid force given plane greatest ground line Hence horizontal plane hyperbola inches inclined plane length lever logarithm measure motion moving nearly ordinate parabola parallel pendulum perpendicular position pressure prob PROBLEM produced prop proportion PROPOSITION quantity radius ratio rectangle resistance right angles right line roots Scholium sides sine solid angle space specific gravity spherical excess spherical triangle square straight line supposed surface tangent theorem theref tion velocity vertical plane vertical projections vibrations weight whole
Popular passages
Page 139 - ... 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...
Page 92 - D'Alembert, was the Precession of the equinoxes and the Nutation of the earth's axis, according to the theory of gravitation.
Page 70 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Page 621 - In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the O's...
Page 238 - 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 11 - 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 32 - 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 205 - 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 302 - ... 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 378 - ... it follows that, by means of it, any one of the three may be expelled out of the calculation, or else brought into it. Also, the momentum, or quantity of motion in a moving body, is qv^ the product of the velocity and matter. It is also to be observed, that the theorems equally hold good for the destruction of motion and velocity, by means of retarding forces, as for the generation of the same, by means of Accelerating forces . And to the following problems, which are all resolved by the application...