| W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...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... | |
| Euclides - 1859
...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
...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
...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
...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 - Education, Higher - 1863
...greater than the base of the other. 8. Equal triangles, on equal bases, in the same straight line, **and on the same side of it, are between the same parallels.** 9. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal... | |
| Euclides - 1864
...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.... | |
| Euclides - 1865
...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 Kne, &c. QED PROP. m.— THEOREM.... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...base, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be **on the same base BC, and on the same side of it** : they shall be between the same parallels. Join AD. A p AD shall be parallel to BC. For if it is not,... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...join AE, BD intersecting at P ; shew that the angle APE is constant. 520. If any number of triangles **on the same base BC, and on the same side of it** have their vertical angles equal, and perpendiculars, intersecting at D, be drawn from B and C on the... | |
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