 | John Playfair - Euclid's Elements - 1835 - 336 pages
...are equal (7. Ax.) ; therefore the triangle ABC is equal to the triangle DEF. PROP. XXXIII. THEOR. Equivalent triangles upon the same base, and upon...the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it ; they are... | |
 | Euclid - 1835 - 540 pages
...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 side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it; they are between... | |
 | Mathematics - 1835 - 684 pages
...in the circumference which bisects the angle between them.] (c) The vertices of all equal spherical triangles upon the same base and upon the same side of it, lie in the circumference of a small circle, such that one equal and parallel to it may be drawn through... | |
 | Mathematics - 1836 - 488 pages
...Triangles upon equal bases, and between the same parallels, are equal to one another. XXXIX. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. XL. Equal triangles on the same side of bases, which are equal and in the same straight line, are between... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...ART. 26. Triangles upon equal bases and between the same parallels are equal, ibid. ART. 27. Equal triangles upon the same base, and upon the same side of it, are between the same parallels, '25. ART. 28. Parallelograms which have equal bases and equal altitudes ire equal, 26. ART. 29. Triangles... | |
 | 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
...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...(Ax. 7) ; therefore the triangle ABC is equal to the triangle DEF. PROPOSITION XXXIX. THEOREM. _ Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC, be upon the same base BC, and upon the same side of it; they are... | |
 | Euclides - 1838 - 264 pages
...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, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it: they shall... | |
 | Euclides - Geometry - 1841 - 378 pages
...triangle ABC is equal to the triangle DEF. Wherefore triangles, &c. QED PROP. XXXIX. THEOR. e, Equal triangles, upon the same base and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it; they shall... | |
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Equal triangles upon the same base, and upon the same side of it, are between the same parallels. 
