The Modern Geometry of the Triangle
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In our eReader you can find the full English version of the book. Read The Modern Geometry of the Triangle 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 Modern Geometry of the Triangle
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To quickly assess the difficulty of the text, read a short excerpt:
Let T-^T^Tg, be the Tangent Triangle, formed by drawing tangents to the ciroumoircle at A, B, G.
Then AT X , jBT 2 , GT t , are concurrent at K.
For, if q, r be the perpendiculars from T t on AO, AB, q _ TfisYnACTs _ ainB _ b r ~~ T X B sin ABT S ~ sin G ~ c ' Hence AT X passes through K ; so also do BT. 2 , CT S .
Note that T x is the point of intersection of the tangents at B and G, whose equations are y/c + a/a = 0, a/a + b/B = 0, so that the n.c. of 2\ are (—a, b, c).
122. The Lemoine Point... A of 1^1,- In the figure of the preceding section, it will be seen that the Lemoine Point K of the inscribed triangle ABG, is the Gergonne Point (32) of T^T,.
Therefore the point M, which is the Gergonne Point of ABG, is the Lemoine Point of XYZ.
But XYZ and 7^1, are homothetic, the centre of similitude being
What to read after The Modern Geometry of the Triangle?
You can find similar books in the "Read Also" column, or choose other free books by William Gallatly to read online
To quickly assess the difficulty of the text, read a short excerpt:
Let T-^T^Tg, be the Tangent Triangle, formed by drawing tangents to the ciroumoircle at A, B, G.
Then AT X , jBT 2 , GT t , are concurrent at K.
For, if q, r be the perpendiculars from T t on AO, AB, q _ TfisYnACTs _ ainB _ b r ~~ T X B sin ABT S ~ sin G ~ c ' Hence AT X passes through K ; so also do BT. 2 , CT S .
Note that T x is the point of intersection of the tangents at B and G, whose equations are y/c + a/a = 0, a/a + b/B = 0, so that the n.c. of 2\ are (—a, b, c).
122. The Lemoine Point... A of 1^1,- In the figure of the preceding section, it will be seen that the Lemoine Point K of the inscribed triangle ABG, is the Gergonne Point (32) of T^T,.
Therefore the point M, which is the Gergonne Point of ABG, is the Lemoine Point of XYZ.
But XYZ and 7^1, are homothetic, the centre of similitude being
What to read after The Modern Geometry of the Triangle?
You can find similar books in the "Read Also" column, or choose other free books by William Gallatly to read online
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