 ... 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 - 1868 - 138 pages
...joins the 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. —... | |
 | E. M. Reynolds - Geometry - 1868 - 172 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 points... | |
 | Anthony Nesbit - 1870 - 578 pages
...ABC 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 figure, DE being parallel to BC, the... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...section shall be parallel to the remaining side of the triangle. Fig. 6. ist. Let the straight line DE be parallel to BC, one of the sides of the triangle ABC, then DE shall divide the sides AB and AC, or these sides produced proportionally, ie so that Join CD and... | |
 | Euclides - 1874 - 342 pages
...straight line 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 BDE is equal... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...straight line which joins the pointt of section i/iall be parallel to the remaining side of the triangle, Let DE be drawn parallel to BC, one of the sides of the triangle A ISC. Then BD shall be to DA, as CE to EA. Join BE, CD. Then the triangle BDE is equal to the triangle... | |
 | Āryabhaṭa - 1878 - 100 pages
...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, are«ut proportionally ; that is, BD is to... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...'.line 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 - Euclid's Elements - 1881 - 236 pages
...homologout, the 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 - 286 pages
...straight 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, because... | |
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