| Benjamin Greenleaf - Geometry - 1863 - 320 pages
...Parallelograms which have two sides and the included angle equal in each, arc them:elves equal. 22. Equivalent **triangles upon the same base, and upon the same side of it, are between the same parallels.** 23. If the middle points of the sides of a trapezoicl, which are not parallel, be joined by a straight... | |
| Euclides - 1864
...equal to the triangle DEF. Wherefore, triangles upon equal bases, &c. QED PROPOSITION XXXIX. THEOREM. **Equal triangles upon the same base and upon the same...upon the same base BC, and upon the same side of it.** Then the triangles ABC, DBC shall be between the same parallels. AD Join AD ; then AD shall be parallel... | |
| Euclides - 1864
...equal to the triangle DEF. "Wherefore, triangles upon equal bases, &c. QED PROPOSITION XXXIX. THEOREM. **Equal triangles upon the same base and upon the same side of it,** art between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon... | |
| Euclides - 1865
...38. Triangles upon equal bases, and between the same parallels, are equal to one another. Prop. 39. **Equal triangles upon the same base, and upon the same side of it,** nre between the same parallels. Prop. 40. Equal triangles upon equal bases in the same straight line,... | |
| John Playfair - Geometry - 1855 - 317 pages
...XXXIX. THEOR. Equal triangles upon the same hast, and ttpon the same side of it, are between the samt **parallels. Let the equal triangles ABC, DBC be upon the same base BC, and** UDOO die same side of it ; they are between the same parallels. Join AD ; AD is parallel to BC ; for,... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...DEF. Wherefore, triangles &c. QED PROPOSITION 39. THEOREM. Equal triangles on the same 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.... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...&c, QED PROPOSITION 40. THEOREM. Equal triangles, on equal bases, in the same straight line, and on **the same side of it, are between the same parallels. Let the equal triangles ABC,** DEF be on equal bases BC, EF, in the same straight line BF, and on the same side of it : they shall... | |
| Robert Potts - 1868 - 410 pages
...QED PROPOSITION XXXIX. THEOREM. Equal triangles upon the same base and upon the same tide of it, an **between the same parallels. Let the equal triangles...upon the same base BC, and upon the same side of it.** Then the triangles ABC, DBC shall be between the same parallels. AD Join AD ; then AD shall be parallel... | |
| Edinburgh univ - 1868
...sides be equal, each to each ; and also the third angle of the one to the third angle of the other. 3. **Equal triangles upon the same base, and upon the same side of it, are between the same parallels.** 4. To divide a given straight line into two parts, so that the rectangle contained by the whole, and... | |
| Benjamin Greenleaf - Geometry - 1868 - 320 pages
...Parallelograms which have two sides and the included angle equal in each, are themselves equal. 22. Equivalent **triangles upon the same base, and upon the same side of it, are between the same parallels.** 23. If the middle points of the sides of a trapezoid, which are not parallel, be joined by a straight... | |
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