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 136
... conic surface , will be zor = -√ ( x2 + y2 ) , or r2 - 2rz + z = x2 + y2 . Now , from this , the nature of curves formed by planes cut . ting the cone in different directions , may readily be inferred . Let it be supposed , first ...
... conic surface , will be zor = -√ ( x2 + y2 ) , or r2 - 2rz + z = x2 + y2 . Now , from this , the nature of curves formed by planes cut . ting the cone in different directions , may readily be inferred . Let it be supposed , first ...
Page 629
... CONIC SECTIONS . PROBLEM I. To construct a conic surface . 1. Draw the ground line AB , in the horizontal plane ; take any point r ' for the centre of the circular base of the cone , and with the radius of the base describe about r ...
... CONIC SECTIONS . PROBLEM I. To construct a conic surface . 1. Draw the ground line AB , in the horizontal plane ; take any point r ' for the centre of the circular base of the cone , and with the radius of the base describe about r ...
Page 630
... cone , in which the curve surface of the cone is inter- sected by a vertical plane passing through the axis of the cone . Thus P " L and P'M are the vertical projections on the opposite slant sides passing through the extremities of the ...
... cone , in which the curve surface of the cone is inter- sected by a vertical plane passing through the axis of the cone . Thus P " L and P'M are the vertical projections on the opposite slant sides passing through the extremities of the ...
Page 631
... conic surface . R T P S " P M L NK 0 A B H R P S E " If we produce Q'K to meet D " H " in Q " , the point a " will ... conic surface . In like manner , if R'M be produced to R " , we have the vertical projection of the. DESCRIPTIVE ...
... conic surface . R T P S " P M L NK 0 A B H R P S E " If we produce Q'K to meet D " H " in Q " , the point a " will ... conic surface . In like manner , if R'M be produced to R " , we have the vertical projection of the. DESCRIPTIVE ...
Page 632
... section of the upper conic surface parallel to the base . If we take any point F ' in R'Q ' produced , and draw D''F ' , OE " at right angles to the ground line AB , it is plain that D " and E " are the vertical projections of the ...
... section of the upper conic surface parallel to the base . If we take any point F ' in R'Q ' produced , and draw D''F ' , OE " at right angles to the ground line AB , it is plain that D " and E " are the vertical projections of the ...
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Common terms and phrases
abscissas altitude axis ball base beam becomes body centre of gravity circle conic surface consequently Corol cosine curve cylinder denote density descending determine diameter direction distance draw earth equa equal equation equilibrio EXAM expression feet find the fluent fluid force given fluxion given plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion moving multiplied nearly ordinates 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 excess spherical triangle square straight line supposed surface tangent theorem theref tion velocity vertex vertical plane vertical projections vibrations weight whole
Popular passages
Page 467 - Or, by an. 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 203 - 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 ;...
Page 247 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 297 - 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 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.
Page 83 - 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...
Page 393 - 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.
Page 252 - 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 148 - 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.