# Instructio Confessarii; In Tres Partes Divisa Pro Supplemento Suae Theologiae Moralis

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## Description

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1744 edition. Excerpt: ...of y = f(x), and of i?2 = (x--a)2 + (y--fS)"', equals 0, or when the contact is of the third order, the radius of curvature is either a maximum or minimum. therefore, the length of the evolute of the elliptic quadrant (5) Radius of curvature and evolute of cycloid. AN=x NP=y-KH-K); The equation to a parabola, of which the axis is perpendicular to the axis of x, and the co-ordinates of the vertex, and--; the latus rectum =-. 29 q q Cor. The general equation to the second degree, or y2 + (ax + b)y + cx2 + ex +f-0, containing five constants, may have a contact of the fourth order, with a curve. And should there be a point at which a2-4c = 0, the osculating curve is a parabola. Immediately before and after this point, a2 must be greater or less than 4c; and therefore the osculating parabola is intermediate between an osculating ellipse and hyperbola. (5) If yx = a2, R=, and equation to evoluteis (a + /3)--(a-)8) = (4a)i. (6) The equation to the catenary is 2y = a (e + e "); shew that the radius of curvature is equal, but opposite, to the normal. R =. a (7) If r = a (l + cos 9); find equation between p and r; 2 /2 IT 4T and shew that radius of curvature =;and chord =--. 3 3 (8) Find the equations between p and r, (l) when r = a (ec + e + ee), (2) when r = a sec V 2rJ-4a2e2c V -V-(-2-1) a2 (9) In the spiral of Archimedes, if r =--shew that the radius = the chord of curvature. (10) Find the evolute of the spiral of which the equation r2-a2 is p2 = e2.-= -The evolute is a similar curve, r e2-a2 '"'-TT?5 and a' = 7" (11) Find the chords of curvature drawn through the centre and focus of an hyperbola. / dx2 (12) If y / 1 +---= -, be the equation to a curve ay1 (the Tractrix); the equation to the evolute...show more

## Product details

• Paperback | 28 pages
• 189 x 246 x 2mm | 68g
• Miami Fl, United States
• English
• black & white illustrations
• 1236576314
• 9781236576316