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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 ... - Side 40
av Euclides - 1841 - 351 sider
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 sider
...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 t SI....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 sider
...Wherefore, triangles, d 7. Ax. fee. QED " " PROP. XXXIX. THEOR. EQUAL triangles upon the same base, knd upon the same side of it, are between the same parallels. Let the equal triangles ABC, DEC be upon the same base BC, and upon the same side of it ; they are between the same parallels. Join...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 sider
...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...Let the equal triangles ABC, DBC be upon the same b? BC, and upon the same side of it ; they are between the " parallels. Join AD ; AD is parallel to...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1813
...Triangles upon equal bases, and between 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 - 528 sider
...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 , 1. the...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - 1816 - 294 sider
...between the same two equal and parallel circles, AH and BIC. r PROP. X. (206.) Theorem. Equal spherical triangles upon the same base, and upon the same side of it, or upon equal arches of the same great circle and towards the same parts, are between the same parallel...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...therefore the triangle ABC is equal to thf triangle DEF. Wherefore triangles, &c. Q, ED 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 tbe point...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...triangle ABC is equal to the triangle ÜEF. therefore triangles, &c. QED Proposition XXXIX. Theorem. ' Equal triangles upon the same base, and upon the same...same base BC, and upon the same side of it ; they aie 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 Arithmetic, Algebra, and Geometry

George Lees - 1826
...base, and between the same 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 - 1827 - 513 sider
...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...Join AD; AD shall be parallel to BC. For, if it is not, through the point A draw * AE parallel to BC, *s1.1. and join EC. The triangle ABC is equal *...
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