Elements of Geometry
Elements of Geometry
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In our eReader you can find the full English version of the book. Read Elements of 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 Elements of Geometry
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To quickly assess the difficulty of the text, read a short excerpt:
Therefore, the triangle DEF is similar to AB (7.
The division may be external. Then GHI is similar to ABG (24) ; and HI is parallel to AB (III, 24, i). In the same way the other sides are respectively parallel, and the tri- angle IIIK is similar to AB C.
28. Theorem. Conversely, when two triangles have their sides respectively parallel, the three lines made through homolo- gous vertices meet at one point.
If the triangles AB C and DEF have their sides respective- ly parallel, it is to be proved... that the lines AD, BE, and CF must meet at one point.
Produce these lines till they meet. Suppose AD and CF meet at G, and AD and BE meet at N.
Since the triangles AGC and D GF are similar (20, n), AC:DF=AG:DG. Likewise, AB:DE= AN : DXT.
ART. 28. ] TRIANGLES. 85 But by hypothesis, Therefore, That is, the line AD is divided in the same ratio at JV and 6r, which is absurd, unless N and G are one point.
The demonstration is the same for the triangle A Center of Similarity is a point similarly situated with reference to two similar figures, whose homologous lines are - parallel.
What to read after Elements of Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Eli T Eli Todd Tappan to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Therefore, the triangle DEF is similar to AB (7.
The division may be external. Then GHI is similar to ABG (24) ; and HI is parallel to AB (III, 24, i). In the same way the other sides are respectively parallel, and the tri- angle IIIK is similar to AB C.
28. Theorem. Conversely, when two triangles have their sides respectively parallel, the three lines made through homolo- gous vertices meet at one point.
If the triangles AB C and DEF have their sides respective- ly parallel, it is to be proved... that the lines AD, BE, and CF must meet at one point.
Produce these lines till they meet. Suppose AD and CF meet at G, and AD and BE meet at N.
Since the triangles AGC and D GF are similar (20, n), AC:DF=AG:DG. Likewise, AB:DE= AN : DXT.
ART. 28. ] TRIANGLES. 85 But by hypothesis, Therefore, That is, the line AD is divided in the same ratio at JV and 6r, which is absurd, unless N and G are one point.
The demonstration is the same for the triangle A Center of Similarity is a point similarly situated with reference to two similar figures, whose homologous lines are - parallel.
What to read after Elements of Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Eli T Eli Todd Tappan to read onlineMoreLess
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