 | Euclides - Euclid's Elements - 1837 - 112 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 - Euclid's Elements - 1837 - 332 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 - 410 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 - 264 pages
...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,... | |
 | Robert Simson - Geometry - 1838 - 434 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 - 332 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 - 316 pages
...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 - 338 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 - 218 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 - 546 pages
...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... | |
| |
EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels. 
