... 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*, * «.i. Books 3-9 - Page 212by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| Joseph Allen Galbraith - 1859
...points of section is parallel to the remaining side of the triangle. PART L Statement — Let DE be **drawn parallel to BC, one of the sides of the triangle ABC.** The sides AB and AC are cut proportionally; that is, BD is to DA, as CE is to EA. Construction. —... | |
| Anthony Nesbit - Measurement - 1859 - 450 pages
...a triangle parallel to one of its sides, it will cut the two other sides proportionally. Let DE be **drawn parallel to BC, one of the sides of the triangle ABC** ; then BD is to DA, as CE to EA. (Euc. VI. 2. Simp. IV. 12. Em. IL 12.) DB THEOREM XI. In the preceding... | |
| Robert Potts - Geometry, Plane - 1860 - 361 pages
...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. AAE Join BE, CD. Then the triangle BDE is equal to the triangle... | |
| Robert Potts - 1864
...which joins 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** Then BD shall be to DA, as CE to EA. Join BE, CD. Then the triangle BDE is equal to the triangle CDE,... | |
| Alexander Kennedy Isbister - 1865
...the remaining side of the triangle. (References— Prop. i. 37, 39 ; v. 7, 9, 11 ; vi. 1.) 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. ED Join BE, CD. DEMONSTRATION Then the triangle BDE is equal to... | |
| Robert Potts - 1865 - 504 pages
...which joins the points of section shall be parallel to the remaining side of the triangle. Let DE\x> **drawn parallel to BC, one of the sides of the triangle ABC.** and cut AB, AC, or these produced in D, E. Then BD shall be to DA, as CE to EA. Join BE, CD. Then the... | |
| Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...which joins the points <\f 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,... | |
| Euclid, Isaac Todhunter - Geometry - 1867 - 400 pages
...join BC, and draw DE parallel to it. AE shall be the part required to be cut off. For, because ED is **parallel to BC, one of the sides of the triangle ABC, therefore** CD is to DA as BE is to EA ; [VI. 2. and, by composition, CA is to AD as BA is to AE. [V. 18. But CA... | |
| Euclid - 1868
...points of section is parallel to the remaining side of the triangle. PART I. Statement — Let DE be **drawn parallel to BC, one of the sides of the triangle ABC.** The sides AB and AC are cut proportionally; that is, BD is to DA, as CE is to E A. Construction. —... | |
| Edward Morris Reynolds - Geometry - 1868 - 112 pages
...there in AM each equal to AF, and so many in LM each equal to DF. THEOREM II. If a straight line LM be **drawn parallel to BC one of the sides of the triangle ABC,** then shall AL_LM_MA AB~ BC~ CA" Divide AL and AB into a number of equal parts as AD, and through the... | |
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