 | Euclides - 1852 - 48 pages
...than the other : they are therefore equal. Which was to be demonstrated. PROP. "VTI. THEOR. If two triangles, on the same base, and on the same side of it, have the sides which terminate in one end of the base equal, those sides which terminate in the other... | |
 | Euclides - Geometry - 1853 - 334 pages
...therefore the triangle ABC is equal to the triangle DEF. Which was to be proved. PEOP. XXXIX. THEOE. Equal triangles on the same base, and on the same side of it shall be between the same parallels. Let the equal triangles ABC, DBC be on the same base BC, and on... | |
 | Robert Potts - 1855 - 1050 pages
...equal to each other. Trisect a triangle by right lines drawn from a point given in one of its sides. 3. Equal triangles, on the same base and on the same side of it, are between the same parallels. 4. In any triangle the square of the side, subtending an acute angle, is less than the sum of the squares... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...Euclid's proof fails when this precaution is not taken, and give a proof in this case. Section 2. 1. Equal triangles on the same base, and on the same side of it, are between the same parallels. 2. If the square described upon one of the sides of a triangle be equal to the squares described upon... | |
 | Euclides - 1855 - 270 pages
...Therefore the triangle BDE is equal to the triangle СDE (V. 9) ; and they are on the same base D E. But equal triangles on the same base and on the same side of it, are between the same parallels (I. 39). Therefore DE is parallel to B С. Wherefore, if a straight line, &c. QED The necessity for... | |
 | 1856 - 428 pages
...figure, etc. QEBf PROPOSITION XL. THEOREM. Equal triangles upon equal bases in the same straight line, and on the same side of it, are between the same parallels. In fig. 40, let the equal triangles ABC and о в F be upon equal bases в с and в F, in the same... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...are equal. Any two triangles of equal altitude, and on equal bases, are equal. Equal triangles upon the same base, and on the same side of it, are between the same parallels. If any two sides of any triangle are intersected by a line parallel to the third side, the intercepted... | |
 | Euclid - 1859 - 150 pages
...Therefore the triangle BDE is equal to the triangle CDE (V. 9); and they are on the same base DE. But equal triangles on the same base and on the same side of it are between the same parallels (I. 39). Therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III—... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...therefore the triangle BDE is equal to the triangle CDE: (v. 9.) and they are on the same base DE: but equal triangles on the same base and on the same side of it, < between the same parallels ; (l. 39.) therefore 1)E is parallel to BC. Wherefore, if a straight line,... | |
 | Royal college of surgeons of England - 1860 - 332 pages
...lines shall be parallel to one another. 5. Equal triangles on equal hases, in the same straight line and on the same side of it, are between the same parallels. 6. If a straight line be divided into any two parts, the squares of the whole line and one of the parts... | |
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DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. 
