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EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 40
by Euclides - 1841 - 351 pages

Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871
...are taken such that BD = AE. Shew that the triangles CBD, ABE are equal. PROPOSITION XXXIX. THEOREM. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. a Let the equal A s ABC, DBC be on the same base BC, and on the same side of it. Join AD. Then must...

The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 285 pages
...base and on the same side of it are between the same parallels. Corollary 3. — Equal parallelograms upon the same base and upon the same side of it are between the same parallels. DEFINITIONS. 49. — If a rectangle be constructed having its adjacent sides respectively equal to...

Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...Z>, Enre taken such that BD = AE. Shew that 'riangles CBD, ABE are equal. PROPOSITION XXXIX. THEOREM. Equal triangles upon the same base, and upon the same...it, are between the same parallels. Let the equal A s ABC, DBC be on the same base BC, and on the same side of it. Join AD. Then trntst AD be II to BC....

The first and second books of Euclid explained to beginners, by C.P. Mason

...parallel to the base upon which they stand.* * This proposition is generally stated thus: — "Equal As upon the same base, and upon the same side of it, are between the same parallels." The meaning of this is just what is stated above, but is less obvious to the beginner. For the construction...

The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...equal to the triangle DEF. Wherefore, triangles upon equal bases, &c. QED PROPOSITION 39. — 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. Construction. Join AD ; then AD shall...

A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...between ike same parallels. * Let the equal triangles ABC, DBC be on the I • same base BC, and on the same side of it : they shall be between the same parallels. Q Join AD. AD shall be AK-- — 7\D «• parallel to BC. For if it is not, through A draw AE parallel...

Pure mathematics, Volume 1

Edward Atkins - 1874
...it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and on the same side of it ; They shall be between the same parallels. CONSTRUCTION. — Join AD ; AD shall be parallel to BC. - For if it is not, through A draw AE v°se-...

Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 pages
...Therefore, triangles, &c. QED Proposition 39. — Theorem. Equal triangles upon the same base, and on the same side of it, are between the same parallels....equal triangles ABC, DBC be upon the same base BC, and on the same side of it ; They shall be between the same parallels. CONSTRUCTION. — Join AD ; AD shall...