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angle appears application arbitrary assume asymptote axis becomes branches called circle co-ordinates coefficients condition constant corresponding curvature curve determine differential differential equation dx dy easily eliminate ellipse equal equation evolute examples expand expression factor formula fraction function given gives Hence independent infinite integral intersection involving length Let the equation limits locus logarithmic maximum means Mémoires method multiplying negative obtain operation origin parallel particular passing perpendicular plane positive powers preceding problem properties quantities radius reduced referred relation respect result roots satisfy Sect sides similar singular solution spiral Substituting supposed surface symbols taken tangent theorem touches trace transformed triangle vanish variables volume whence
Сторінка 133 - ... non inconcinne adhiberi posse. Quoniam enim semper sibi similem et eandem spiram gignit, utcunque volvatur, evolvatur, radiet ; hinc poterit esse vel sobolis parentibus per omnia similis emblema...
Сторінка 120 - AS' is traced a second time ; thus, the curve is traced twice by one revolution of the radius-vector. THE CONCHOID OF NICOMEDES.* 150. This curve was invented by Nicomedes, who lived about the second century of our era, and was, like the preceding, first formed for the purpose of solving the problem of finding two mean proportionals, or the duplication of the cube ; but it is more readily applicable to another problem not less celebrated among the ancients, that of the trisection of an angle. The...
Сторінка 133 - Lumine emanans eidem o.adötoi,- existit, qualiscumque adumbratio. Aut, si mavis, quia Curva nostra mirabilis in ipsa mutatione semper sibi constantissime manet similis et numero eadem, poterit esse vel fortitudinis et...
Сторінка 117 - Find that point within a triangle, from which if lines be drawn to the angular points, the sum of their squares shall be a minimum.
Сторінка 430 - II. (if + z* — x*} p — 12. Required the equation of the surface which cuts at right angles all the spheres which pass through the origin of coordinates and have their centres in the axis of x. It will be found that this leads to the partial differential equation of the last problem.
Сторінка 440 - Find the surface in which the coordinates of the point where the normal meets the plane of xy are proportional to the corresponding coordinates of the surface.
Сторінка 117 - To find a point within a triangle from which if lines be drawn to the angular points their sum may be the least possible.
Сторінка 409 - ... be lengthened. Newton found that the length of the polar must be to that of the equatorial canal as 229 to 230, or that the earth's polar radius must be seventeen miles less than its equatorial radius : that is, that the figure of the earth is an oblate spheroid, formed by the revolution of an ellipse round its lesser axis. Hence it follows, that the intensity of gravity at any point of the earth's surface is in the inverse ratio of the distance of that point from the centre, and consequently...