| Great Britain. Admiralty - Geometry - 1846
...double the /\ ABC, or double the ^ EFG, which is its equal, by last Cor. PROP. XXXVI. THEOR. 39. 1 Eu. **Equal triangles upon the same base, and upon the same...side of it, are between the same parallels. Let the** = <£^s ABC, DEC, be on the same base BC, and on the same side of it ; then the will be between the... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 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... | |
| Great Britain. Admiralty - Geometry - 1846
...double the ^\ ABC, or double the ^ EFG, which is its equal, by last Cor. PROP. XXXVI. THEOR. 39. lEu. **Equal triangles upon the same base, and upon the same side of it, are between the** name parallels. Let the = ^s ABC, DEC, be on the same base BC, and on the same side of it; then the... | |
| Euclides - 1846
...upon S,c, QED 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 shall... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...(a) p. 31; (4) p. 36 ; (c)p.34; (d)ax. 7. 89 Th. Equal triangles (ABC, DBC), upon the same base (BC), **and upon the same side of it, are between the same parallels.** Join AD;—AL» is parallel to BC: for if not, through the point A draw AE parallel to BC (a), aud... | |
| Euclides - 1847
...bisected by a st. line AG drawn through one of the L ' BAC. — QEF PROP. XXXIX. THEOR. PART. ENUN. — **Equal triangles upon the same base, and upon the same side of it, are between the same parallels.** PART. ENUN. — Let the = AS ABC, DBC be upon the same base BC, and upon the same side of it ; then... | |
| Euclides - 1848
...Triangles upon equal bases and between the same parallels, are equal to one another. PROP. XXXIX. THEOREM. **Equal triangles upon the same base and upon the same side of it, are between the same parallels.** PROP. XL. THEOREM. Equal triangles upon equal bases, in the same straight line, and towards the same... | |
| Euclides, Thomas Tate - 1849 - 108 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...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... | |
| University of Durham - Education, Higher - 1851
...line. 2. Straight lines which are parallel to the same straight line are parallel to each other. 3. **Equal triangles upon the same base and upon the same side of it are between the same parallels.** 4. If a straight line be divided into any two parts, the square of the whole line is equal to the square... | |
| 1867
...parallelogram by lines drawn from a givtu point in one of its sides. SECTION IV. 1. Eqnal triangles which are **upon the same base and upon the same side of it are between the same parallels.** If of the four triangles into which the diagonals divide a trapezium, any two opposite ones are eqnal,... | |
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