| Walter Henry Burton - Astronomy - 1828 - 68 pages
...hand, equal triangles Prop. xii. upon the same base (or upon equal bases in the same straight line) **and upon the same side of it, are between the same parallels.** For if the straight line which joins the vertices of the two triangles be not parallel to the base,... | |
| Pierce Morton - Geometry - 1830 - 272 pages
...in the circumference which bisectsthe 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... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...PROPOSITION XL. See Note. THEOREM. — Equal triangles, upon equal bases in ihe same straight line, and on **the same side of it, are between the same parallels. Let the** triangles ABC, EFD, which are upon equal bases BC and EF in the same straight line BF, and on the same... | |
| Euclides - 1834
...is equal to the • 7 Ax. triangle DEF. Wherefore, triangles, &c. QED PROPOSITION XXXIX. THEOn. — **Equal triangles upon the same base, and upon the same...Join AD : AD shall be parallel to BC. For if it is** not, through the point A, draw * AE parallel to BC, and join EC. s 31. i. The triangle ABC is equal... | |
| Euclid - 1835 - 513 pages
...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...the 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 - 1835 - 316 pages
...(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...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... | |
| Mathematics - 1835
...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 - 472 pages
...XXXVIII. 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 - 128 pages
...equal, 24. 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... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...equal (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...the same base BC, and upon the same side of it; they** are between the same parallels. rallels BC, AE. But the triangle ABC is equal to the triangle BDC ;... | |
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