 ... proportionally : and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section, shall be parallel to the remaining side of the triangle.  A Treatise on Practical Gauging - Page 64by Anthony Nesbit, W. Little - 1822Full view - About this book
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...straight line 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 - Mathematics, Greek - 1908 - 456 pages
...the line joining the points of section will be parallel to the remaining side of the triangle. For let DE be drawn parallel to BC, one of the sides of the triangle ABC ; I say that, as BD is to DA, so is CE to EA. For let BE, CD be joined. Therefore the triangle BDE... | |
 | Anthony Nesbit - Measurement - 1859 - 482 pages
...to one of its sides, it will cut the two other sides proportionally. Let DE be drawn parallel to EC, one of the sides of the triangle ABC ; then BD is to DA, as CE to EA. (Euc. VI. 2. Simp. IV. 12. Em. IL12.) D 14 THEOREM XL In the preceding figure, DE being parallel to BC, the triangles ABC, ADE are... | |
 | Electrical engineering - 1874 - 424 pages
...ratios A 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... | |
 | Euclid - 452 pages
...the line joining the points of section will be parallel to the remaining side of the triangle. For let DE be drawn parallel to BC, one of the sides of the triangle ABC ; I say that, as BD is to DA, so is CE to EA. For let BE, CD be joined. Therefore the triangle BDE... | |
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