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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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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...respectively = these equal oms and .'. = each other. PROPOSITION XXXIX. (Argument ad absurdum.) Theorem. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Steps of the Demonstration. Suppose that AD is not || BC, but that some other line, as AE, is || BC....
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 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 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. K) AE parallel to...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 pages
...triangles, &c. 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 are...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...triangle ABC is equal to the triangle DEF. Wherefore triangles, &c. QED PROP. XXXIX. THEOR. 3j 1 *IT! i. Equal triangles upon the same base, and upon the same...side of it: they shall be between the same parallels. Draw AD ; AD shall be parallel to BC. For if it is not, through the point A draw* AE parallel to BC,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - Geometry - 1838 - 416 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...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...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...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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...equal or equivalent to the triangle DEF. Wherefore triangles, &c. QED PROP. XXXIX. THEOR. EQUIVALENT triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equivalent triangles ABC, DBC be upon the same base B c, and upon the same side of it : they are between...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 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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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...triangle ABC is equal to the triangle DEF. Wherefore triangles, &c. QED PROPOSITION XXXIX. THEOR. — Equal triangles upon the same base, and upon the same...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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...equal to the triangle DEF. Wherefore, triangles upon equal bases, &c. QEU 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; AD shall be parallel to...
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