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" Equal triangles upon the same base, and upon the same side of it, are between the same parallels. "
Dialogues on the First Principles of the Newtonian System - Page 19
by Walter Henry Burton - 1828 - 68 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...triangle DEF. Wherefore, triangles, &c. QED PROP. XXXIX. THEOR. EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it ; they are...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...the same parallels, are equal to one another. Prop. XXXIX. Theor. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Prop. XL. Theor. Equal triangles upon equal bases, in the same straight line, and towards the same...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...triangle DEF. Wherefore triangles, &c. QED PROP. XXXIX. THEOR. EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it ; they are...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...triangle DEF. Wherefore triangles, &Lc. QED PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it ; they are...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...ÜEF. therefore triangles, &c. QED Proposition XXXIX. Theorem. ' Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it ; they aie...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...parallels, the parallelogram is double of the triangle. Cor. 3. Equivalent triangles upon the same base, and upon the same side of it, are between the same parallels. Book I. a 14.1 b 11. 1. c2. ELEMENTS PROP. XVI. THEOREM. Parallelograms, CABD, EFHG, upon equal bases,...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...triangle DEF. Wherefore triangles, &c. QED PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it : they shall...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...bases, and between the same parallels, are equal to-one another : and conversely, equal triangles, upon the same base, or upon equal bases in the same straight line, and towards the same paru, are between the same parallels. The first part of the proposition is manifest...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...bases, and between the same parallels, are equal to one another : and conversely, equal triangles, upon the same base, or upon equal bases in the same straight line, and towards the same parts, are between the same parallels. The first part of the proposition is manifest...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...triangle DEF. Wherefore, " triangles" &c. QED PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the same side of it; they are between...
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