| Euclides - Euclid's Elements - 1837 - 88 pages
...respectively = these equal oms and .'. = each other. PROPOSITION XXXIX. (Argument ad absurdum.) Theorem. **Equal triangles upon the same base, and upon the same side of it, are between the same parallels.** Steps of the Demonstration. Suppose that AD is not || BC, but that some other line, as AE, is || BC.... | |
| John Playfair - Geometry - 1837 - 318 pages
...things are equal (7. Ax.) ; therefore the triangle ABC is equal to the triangle DEF. PROP. XXXIX. THEOR. **Equal triangles upon the same base, and upon the same side of it, are between the same parallels.** Join AD ; AD is parallel to BC ; for, if it is not, through the point A draw (31. K) AE parallel to... | |
| Euclid, James Thomson - Geometry - 1837 - 390 pages
...triangles, &c. PROP. XL. THEOR. EQUAL triangles upon 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 upon equal bases BC, EF, in the same straight line BF, and on the same side of it ; they are... | |
| Euclides - 1838
...triangle ABC is equal to the triangle DEF. Wherefore triangles, &c. QED PROP. XXXIX. THEOR. »3j 1 *IT! i. **Equal triangles upon the same base, and upon the same...side of it: they shall be between the same parallels.** Draw AD ; AD shall be parallel to BC. For if it is not, through the point A draw* AE parallel to BC,... | |
| Euclid, Robert Simson - Geometry - 1838 - 416 pages
...therefore the triangle ABC is equal to the triangle DEF. Wherefore triangles, &c. QED PROP. XXXIX. THEOR. **EQUAL triangles upon the same base, and upon the same...same base BC, and upon the same side of it ; they** are between the same parallels. Join AD; AD is parallel to BC : for, if it is not, through the point... | |
| John Playfair - Euclid's Elements - 1842 - 317 pages
...are equal (7. Ax.) ; therefore the triangle ABC is equal to the triangle DEF. , PROP. XXXIX. THEOR. **Equal triangles upon the same base, and upon the same...same base BC, and upon the same side of it ; they** are between the same parallels. Join AD ; AD is parallel to BC ; for, if it is not, through the point... | |
| Euclides - 1842
...equal or equivalent to the triangle DEF. Wherefore triangles, &c. QED PROP. XXXIX. THEOR. EQUIVALENT **triangles upon the same base, and upon the same side of it, are between the same parallels. Let the** equivalent triangles ABC, DBC be upon the same base B c, and upon the same side of it : they are between... | |
| John Playfair - Euclid's Elements - 1844 - 317 pages
...things are equal (7. Ax.) ; therefore the triangle ABC is equal to the triangle DEF. PROP. XXXIX. THEOR. **Equal triangles upon the same base, and upon the same side of it, are between the same parallels.** Join AD ; AD is parallel to BC ; for, if it is not, through the point A draw (31. 1.) AE parallel to... | |
| Euclid - Geometry - 1845 - 199 pages
...triangle ABC is equal to the triangle DEF. Wherefore triangles, &c. QED PROPOSITION XXXIX. THEOR. — **Equal triangles upon the same base, and upon the same...same base BC, and upon the same side of it : they** are between the same parallels. Join AD ; AD is parallel to BC ; for, if it is not, through the point... | |
| Euclides - 1845
...equal to the triangle DEF. Wherefore, triangles upon equal bases, &c. QEU 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; AD shall be parallel to... | |
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