Textbook of Geometry
Textbook of Geometry
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In our eReader you can find the full English version of the book. Read Textbook 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 Textbook of Geometry
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SIMILAR TBIANQLBS. 147 But hj hypothesis, AB:A'B' = £C.£'0'. The last two proportions have the first three terms equal, each to each ; therefore the fourth terms are equal ; that is, UM= B'C. Hence in the A AHMand A'B'C, EH^BC, AE=A'B<, and^^=^'C». .-. A AEB:= a A'B^O', § 160 {havmg three sides of the one equal respectively to three sides of the other). But A AEH is Bimilar to A ABC. .-. A A^B^C^ is similar to A ABQ. q. e. d. 326. Scholium. The primary idea of similarity is likeness of form ; and the two conditions necessary to similarity are : I. For every angle in one of the figures there must be an equal angle in the other, and II. The homologous sides must be in proportion. In the case of triangles, either condition involves the other, but in the case of other poli/gons, it does not follow that if one condition exist the other does also. Q' R' Thus in the quadrilaterals Q and Qf, the homologous sides are proportional, but the homologous angles are not equal. In the quadrilaterals B and B' the homologous angles are equal, but the sides are not proportional.
What to read after Textbook of Geometry?
You can find similar books in the "Read Also" column, or choose other free books by George Albert Wentworth to read online
To quickly assess the difficulty of the text, read a short excerpt:
SIMILAR TBIANQLBS. 147 But hj hypothesis, AB:A'B' = £C.£'0'. The last two proportions have the first three terms equal, each to each ; therefore the fourth terms are equal ; that is, UM= B'C. Hence in the A AHMand A'B'C, EH^BC, AE=A'B<, and^^=^'C». .-. A AEB:= a A'B^O', § 160 {havmg three sides of the one equal respectively to three sides of the other). But A AEH is Bimilar to A ABC. .-. A A^B^C^ is similar to A ABQ. q. e. d. 326. Scholium. The primary idea of similarity is likeness of form ; and the two conditions necessary to similarity are : I. For every angle in one of the figures there must be an equal angle in the other, and II. The homologous sides must be in proportion. In the case of triangles, either condition involves the other, but in the case of other poli/gons, it does not follow that if one condition exist the other does also. Q' R' Thus in the quadrilaterals Q and Qf, the homologous sides are proportional, but the homologous angles are not equal. In the quadrilaterals B and B' the homologous angles are equal, but the sides are not proportional.
What to read after Textbook of Geometry?
You can find similar books in the "Read Also" column, or choose other free books by George Albert Wentworth to read online
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