| John Playfair - Euclid's Elements - 1856 - 318 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
...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.... | |
| Euclides - 1858
...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
...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 - 361 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
...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
...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 - 490 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 - 490 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... | |
| Euclides - 1863
...obtained ; the product of the base and altitude gives the area of a parallelogram : PROP. 39. — TIIEOK. **Equal triangles upon the same base and upon the same side of it are between the same parallels.** CON.— Pst.'l, P. 31.— DEM.— P. 37, Ax. 1. Letthe AS ABC, qual, ittne ASAUU, -Lii3u,De equal,... | |
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