The differential and integral calculus, containing differentiation, integration, development, series, differential equations, differences, summation, equations of differences, calculus of variations, definite integrals,--with applications to algebra, plane geometry, solid geometry, and mechanics Also, Elementary illustrations of the differential and integral calculus . d made as follows, to as many different species of pro-jection as may be wanted. The card or blockCOBVW admits of the three axes being immediatelylaid down by placing it on the paper and running apencil along the edges CO, OB, a
The differential and integral calculus, containing differentiation, integration, development, series, differential equations, differences, summation, equations of differences, calculus of variations, definite integrals,--with applications to algebra, plane geometry, solid geometry, and mechanics Also, Elementary illustrations of the differential and integral calculus . d made as follows, to as many different species of pro-jection as may be wanted. The card or blockCOBVW admits of the three axes being immediatelylaid down by placing it on the paper and running apencil along the edges CO, OB, and into the slit of parts answering to the projections of equalparts ate laid down along the three axes, and repeatedon the unoccupied sides. The position of a point•*> whose coordinates are given is then immediately foundby taking off the coordinates on the axes, and using a parallel ruler. The best wayof laying down the different scales of equal parts is by observing that their units onOG, OE, and OF must be as the square roots of the sines of double the angles atG, E, and F: also the angle at G is the supplement of EOF, &c. See the Cam-bridge Mathematical Journal, vol. ii. p. 92. 111 TTTTrrfu Trm-i ; 5 ; : .0 ~ A-rr >!>>^ U 1 liiirmifii ,,V>-^ APPLICATION TO GEOMETRY OF THREE DIMENSIONS. 437 Q K Q TJ\^ 1— Jmu Y. The diagram before, us represents in three positions the projection ofthe lines of curvature of an elliptic paraboloid, to which we shall pre-sently come. In the middle figure, O (hidden by the solid) is the origin,and the line drawn to the eye is meant to make equal angles with OXand OY, and a much larger angle with OZ. This figure contains onequarter of the frustum of the paraboloid. On the right we see twoquarters projected on the plane of ZX; the axis of y passes through theeye and is invisible, and the point Q of the last figure is now confoundedwith Z. On the left we also see two quarters projected on the plane ofZY, the axis of x i
Size: 1965px × 1272px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthorsocietyforthediffusio, bookcentury1800, bookdecade1840
