 | John Playfair - Euclid's Elements - 1856 - 346 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...equal triangles ABC, DBC be upon the same base BC, and uoon the same side of it ; they are between the same parallels. "Join AD ; AD is parallel to BC ; for,... | |
 | Euclides - 1856 - 168 pages
...the point G will coincide with F, and the line EG with EF; wherefore EG or BC is equal to E F. XLII. Equal triangles upon the same base, and upon the same...between the same parallels. Let the equal triangles ABC, DBG (Fig. 33) be upon the same base BC, and upon the same side of it ; they are between the same parallels.... | |
 | 1857 - 400 pages
...parallelogram equal to a given triangle, and having an angle equal to a given rectilineal angle. Quest. 2. Equal triangles upon the same base and upon the same side of it, are between the same parallels. Quest. 3. If one side of a triangle be produced, the exterior angle is greater than either of the interior... | |
 | Euclides - 1858 - 248 pages
...CHEB. the triangle AB ( ' has been bisected from the point H by the line HE. QKF PROP. 39.— TIIEOR. Equal triangles upon the same base and upon the same side of it are between the same parallels. CONSTRUCTION. — Pst. 1. A line may be drawn between two points. 1*. ,-il. Through a given point to... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1859 - 140 pages
...ad absurdum, and illustrate it by Euclid, Book I., Prop. 39, "Equal triangles, upon the same4Sase, and upon the same side of it, are between the same parallels." Is the reducuo adabstirdnmofless force than the direct forms of inference ? 3. Construct an isosceles... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...equal to the triangle DEF. Wherefore, triangles upon equal bases, &c. QED PROPOSITION XXXIX. THEOREM. Equal triangles upon the same base and upon the same...upon the same base BC and upon the same side of it. Then the triangles ABC, DBC shall be between the same parallels. AD Join AD ; then AD shall be parallel... | |
 | Euclides - 1860 - 288 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 side of it, are between the same parallels. Given the equal triangles ABC and DBC, upon the same base BC, and upon the same side of it; to prove... | |
 | Euclides - 1861 - 464 pages
...to one another; and those to which the same M has the some R are eq. to one another. 39, 1. Eq. Дs upon the same base and upon the same side of it are between the same parallels. E. l C. Hyp. 1. Cone. C. CASE I. Let DE be [| BC, one of the sides of Д ABC; and let DE cut the other... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...Parallelograms which have two sides and the included angle equal in each, are themselves equal. 22. Equivalent triangles upon the same base, and upon the same side of it, are between the same parallels. 23. If the middle points of the sides of a trapczoid, which are not parallel, be joined by a straight... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...Parallelograms which have two sides and the included angle equal in each, are themselves equal. 22. Equivalent triangles upon the same base, and upon the same side of it, are between the same parallels. 23. If the middle points of the sides of a trapezoid, which are not parallel, be joined by a straight... | |
| |
EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels. 
