A sequel to the first six books of the Elements of Euclid, containing an easy introduction to modern geometry, with numerous examples. By John Casey.

BOOK VI. 101 y, 8. Then, by Prop. 6, we have the following equalities:AC = A'C' p AC -, B'D'. p AB - a C'D' p CD = CID' Hence multiplying, and remembering that the rectangle pfy is equal to the rectangle as (see Prop. 11, Section I., Book III.), we get AC. BD A'C'. B'D' AB. CD A'B'. C'D' Cor. 1.AC. BD: AB. CD: AD. BO: C' B: A. B'D B'. C'D': A'D'. B'C'. Cor. 2.-If the points A, B, C, D form a harmonic system, the points A', B', C', D' form a harmonic system. In other words, the inverse of a harmonic system of points forms a harmonic system. Cor. 3. —If AB = BC; then the points A, B', C', 0 form a harmonic system of points. Prop. 9.-If two circles be inverted into two others, the square of the common tangent of the first pair, divided by the rectangle contained by their diameters, is equal to the square of the common tangent of the second pair, divided by the rectangle contained by their diameters?

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Title
A sequel to the first six books of the Elements of Euclid, containing an easy introduction to modern geometry, with numerous examples. By John Casey.
Author
Casey, John, 1820-1891.
Canvas
Page 96
Publication
Dublin,: Hodges, Figgis & co.; [etc., etc.]
1888.
Subject terms
Geometry

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"A sequel to the first six books of the Elements of Euclid, containing an easy introduction to modern geometry, with numerous examples. By John Casey." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/acv1576.0001.001. University of Michigan Library Digital Collections. Accessed May 24, 2025.
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