 | Euclides - 1848 - 52 pages
...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... | |
 | Euclid, Thomas Tate - 1849 - 120 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 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... | |
 | University of Durham - Education, Higher - 1851 - 222 pages
...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 - 336 pages
...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,... | |
 | Euclides - 1852 - 152 pages
...triangle ABC is equal to the triangle DEF. "Wherefore triangles, &c. QED BOOK I. 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, DEC be upon the same base BC, and upon the same side of it; they arc between... | |
 | Euclides - 1852 - 48 pages
...given number of parts, and drawing right lines to the vertex of the triangle. 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 в A c and в D c be upon the same base вc, and on the same .--./ side of... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...ABC is equal to the triangle DEF. Wherefore triangles etc. Q.. E, D. PROPOSITION 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, DEC be upon the same base BC, and upon the same side of it : they are... | |
 | Euclides - 1853 - 146 pages
...triangle ABC is equal to the triangle DEF. Wherefore, triangles, &c. QED PROP. XXXIX. THEOREM. Equal triangles upon the same base and upon the same side of it, are Let the equal triangles ABC, DBC, be upon the same base BC> and upon the same side of it ; they are... | |
 | Popular educator - 1852 - 1272 pages
...parallel lines should be assumed as an axiom, on which reasonings on such lines may be founded ? 7. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Hence show that a triangle may be bisected by a line drawn "rom any point in one of its sides. 8. To... | |
 | Euclides - 1855 - 270 pages
...into equal triangles on opposite sides of the segments of the diagonal. PROP. XXXIX. THEOREM. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equal triangles ABС, DB С, be upon the sате base B С, and upon the sате side of it.... | |
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Equal triangles upon the same base, and upon the same side of it, are between the same parallels. 
