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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
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846
...double the /\ ABC, or double the ^ EFG, which is its equal, by last Cor. PROP. XXXVI. THEOR. 39. 1 Eu. Equal triangles upon the same base, and upon the same...side of it, are between the same parallels. Let the = <£^s ABC, DEC, be on the same base BC, and on the same side of it ; then the will be between the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 317 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 side of it, are between the same parallels. Join AD ; AD is parallel to BC ; for, if it is not, through the point A draw (31. 1.) AE parallel to...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846
...double the ^\ ABC, or double the ^ EFG, which is its equal, by last Cor. PROP. XXXVI. THEOR. 39. lEu. Equal triangles upon the same base, and upon the same side of it, are between the name parallels. Let the = ^s ABC, DEC, be on the same base BC, and on the same side of it; then the...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...upon S,c, QED PROP. XL. THEOR. Equal triangles upon equal bases, in the same straight line, and on the same side of it, are between the same parallels. Let the equal triangles, ABC, DEF, be upon equal bases BC, EF, in the same straight line BF, and on the same side of it : they shall...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...(a) p. 31; (4) p. 36 ; (c)p.34; (d)ax. 7. 89 Th. Equal triangles (ABC, DBC), upon the same base (BC), and upon the same side of it, are between the same parallels. Join AD;—AL» is parallel to BC: for if not, through the point A draw AE parallel to BC (a), aud...
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The First Book of Euclid's Elements, Simplified, Explained, and Illustrated ...

Euclides - 1847
...bisected by a st. line AG drawn through one of the L ' BAC. — QEF PROP. XXXIX. THEOR. PART. ENUN. — Equal triangles upon the same base, and upon the same side of it, are between the same parallels. PART. ENUN. — Let the = AS ABC, DBC be upon the same base BC, and upon the same side of it ; then...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...Triangles 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...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides, Thomas Tate - 1849 - 108 pages
...therefore 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...the same base BC, and upon the same side of it; they are between the same parallels. Join AD: AD is parallel to BC ; for, if it is not, through the point...
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University of Durham

University of Durham - Education, Higher - 1851
...line. 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...
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Papers for the schoolmaster, Volume 3

1867
...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,...
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