... be parallel to the remaining side of the triangle. Let DE be drawn parallel to BC, one of the sides of the triangle ABC : BD is to DA, as CE to EA. Join BE, CD ; Then the triangle BDE is equal to the triangle CDE*, * Ğ.i. Books 3-9 - Page 212by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| William Burness - 1870
...in that semicircle is a right angle (Euc. iii. 31 ; Simp. iii. 13; Em. vi. 14). THEOREM X. Lst DE be **drawn parallel to BC, one of the sides of the triangle ABC** ; then BD is to DA as CE to EA (Euc. vL 2 ; Simp. iv. 12 j Em. ii. 12). THEOREM XI. In the preceding... | |
| James Martin (of the Wedgwood inst, Burslem) - 1874
...which joins the points of section shall be parallel to the remaining side of the triangle. Let DE be **drawn parallel to BC. one of the sides of the triangle ABC.** • Then BD shall be to DA, as CE to EA. Construction. Join BE, CD. Demonstration. Then the triangle... | |
| Āryabhaṭa - 1878
...t!f. one side, so are the corresponding segments in the other side to one another. First, let DE'be **drawn parallel to BC, one of the sides of the triangle ABC.** The sides AB A and AC.', or, AB,- AC produced towards A, areĞut proportionally ; that is, BD is to... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...which joint the points of section, shall be parallel to the remaining side of the triangle. Let DE be **drawn parallel to BC, one of the sides of the triangle ABC:** BD shall be to DA as CE is to EA. Join BE, CD. Then the triangle BDE is equal to the triangle CDE,... | |
| Euclides - 1881
...straight line which joint the pointt of tection is parallel to the base of the triangle. Let DE be **drawn parallel to BC, one of the sides of the triangle ABC.** The sides AB and AC or AB and AC produced, are cut proportionally ; that is, BD is to DA, asCEistoEA.... | |
| Isaac Sharpless - Geometry - 1882 - 266 pages
...line which joins the points of section will be parallel to the other side of the triangle. Let DE be **drawn parallel to BC, one of the sides of the triangle ABC;** then BD : DA : : CE : EA. E CD EB Join BE, CD ; then the triangle BDE is equal to the triangle CDE,... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...which joint the points of section, shall be parallel to the remaining tide of the triangle. Let DE be **drawn parallel to BC, one of the sides of the triangle ABC:** BD shall be to DA as CE is to EA. Join BE, CD. Then the triangle BDE is equal to the triangle CDE,... | |
| Euclid
...each of the parallelograms EG, HK is similar both to the whole ABCD and to the other. For, since EF **has been drawn parallel to BC, one of the sides of the triangle ABC,** proportionally, as BE is to EA, so is CF to FA. [vi. 2] Again, since FG has been drawn parallel to... | |
| Electric engineering - 1874
...b : fr B, Ad : <ID, Ac : cC are all equal. We have then the following theorem : — If a line DE be **drawn parallel to BC, one of the sides of the triangle ABC,** then FIG. 19. AD:DB::AE:EC. Of course we get in the same way that AB : AD :: AC : AE. Or the same thing... | |
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