The Elements of Cordinate Geometry
The Elements of Cordinate Geometry
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In our eReader you can find the full English version of the book. Read The Elements of Cordinate Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Elements of Cordinate Geometry
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Bisect the angle between the focal radii, and it will be either a normal or a tangent, (Arts. 108 and 117). If the latter, erect a perpendicular as stated in the preceding case.
3. By means of the subnormal. For the ellipse and hy- perbola we proceed as follows : FIG. 87.
We have, (Art.
in which x = CD. To construct this take the lines CA and CB, Fig. 89, making any convenient angle with each other. Make CA a, CB = b, and CD x'. Join B and A and draw Z>7parallel toAB. Take CG equal to CJ and dr...aw GK parallel G D A FIG. 89.
78 CONIC SECTIONS. [118.
to AB ; CK will be the required subnormal. For we have CJ CBb r_&, CK CJ CJ=CG which is the value sought. The distance CK being laid off from D, Figs. 87, 88, in the proper direction gives the point N, and PN will be the required normal.
For the parabola let P be the point. Drop the perpen- dicular PD to the axis of the curve, and lay off DN equal to one-half of the parameter of the curve ; then will the line PN be the required normal.
[This method also furnishes an easy mode of drawing a tangent to a .
What to read after The Elements of Cordinate Geometry?
You can find similar books in the "Read Also" column, or choose other free books by De Volson Wood to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Bisect the angle between the focal radii, and it will be either a normal or a tangent, (Arts. 108 and 117). If the latter, erect a perpendicular as stated in the preceding case.
3. By means of the subnormal. For the ellipse and hy- perbola we proceed as follows : FIG. 87.
We have, (Art.
in which x = CD. To construct this take the lines CA and CB, Fig. 89, making any convenient angle with each other. Make CA a, CB = b, and CD x'. Join B and A and draw Z>7parallel toAB. Take CG equal to CJ and dr...aw GK parallel G D A FIG. 89.
78 CONIC SECTIONS. [118.
to AB ; CK will be the required subnormal. For we have CJ CBb r_&, CK CJ CJ=CG which is the value sought. The distance CK being laid off from D, Figs. 87, 88, in the proper direction gives the point N, and PN will be the required normal.
For the parabola let P be the point. Drop the perpen- dicular PD to the axis of the curve, and lay off DN equal to one-half of the parameter of the curve ; then will the line PN be the required normal.
[This method also furnishes an easy mode of drawing a tangent to a .
What to read after The Elements of Cordinate Geometry?
You can find similar books in the "Read Also" column, or choose other free books by De Volson Wood to read onlineMoreLess
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