 | Euclides - 1855 - 270 σελίδες
...triangle BDE is equal to the triangle СDE (V. 9) ; and they are on the same base D E. But equal triangles on the same base and on the same side of it, are between the same parallels (I. 39). Therefore DE is parallel to B С. Wherefore, if a straight line, &c. QED The necessity for... | |
 | Robert Potts - 1855 - 1050 σελίδες
...Trisect a triangle by right lines drawn from a point given in one of its sides. 3. Equal triangles, on the same base and on the same side of it, are between the same parallels. 4. In any triangle the square of the side, subtending an acute angle, is less than the sum of the squares... | |
 | 1856 - 428 σελίδες
...figure, etc. QEBf PROPOSITION XL. THEOREM. Equal triangles upon equal bases in the same straight line, and on the same side of it, are between the same parallels. In fig. 40, let the equal triangles ABC and о в F be upon equal bases в с and в F, in the same... | |
 | W. Davis Haskoll - 1858 - 422 σελίδες
...are equal. Any two triangles of equal altitude, and on equal bases, are equal. Equal triangles upon the same base, and on the same side of it, are between the same parallels. If any two sides of any triangle are intersected by a line parallel to the third side, the intercepted... | |
 | Euclid - 1859 - 150 σελίδες
...triangle BDE is equal to the triangle CDE (V. 9); and they are on the same base DE. But equal triangles on the same base and on the same side of it are between the same parallels (I. 39). Therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III—... | |
 | Royal college of surgeons of England - 1860 - 332 σελίδες
...lines shall be parallel to one another. 5. Equal triangles on equal hases, in the same straight line and on the same side of it, are between the same parallels. 6. If a straight line be divided into any two parts, the squares of the whole line and one of the parts... | |
 | Euclides - 1861 - 464 σελίδες
...Prop. also enables us from any . in a side of а Д to divide it into two eq. parts. 39. 120. Eq. Д8 on the same base and on the same side of it are between the same parallels. The loci of the vertices of eq. Дз on the same base, form a st.linc 40. 121. Eq. дз on eq. bases... | |
 | Euclides - 1862 - 172 σελίδες
...halves of the same are equal to one another,' (ax 7.) PROP. XXXIX.— THEOREM. Equal triangles upon the same base and on the same side of it, are between the same parallels. (References — Prop. i. 31,37; ax. !._) Let the equal triangles ABC, DEC, be upon the same base BC,... | |
 | University of Oxford - 1863 - 316 σελίδες
...three interior angles of every triangle are together equal to two right angles. 6. Equal triangles on the same base, and on the same side of it, are between the same parallels. 7. If a straight line be divided into any two parts, the rectangles contained by the whole and each... | |
 | Euclides - 1864 - 448 σελίδες
...triangle BDE is equal to the triangle CDE: (v. 9.) and they are on the same base DE: but equal triangles on the same base and on the same side of it, are between the same parallels ; (I. 39.) therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III.... | |
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DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. 
