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" Equal triangles upon the same base, and upon the same side of it, are between the same parallels. "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 303
by Benjamin Greenleaf - 1862 - 490 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...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 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) cyclopŠdia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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 pages
...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 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 Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...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 pages
...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 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 - 372 pages
...ABC is equal to the triangle ▄EF. 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 - 272 pages
...the same 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 - Trigonometry - 1827 - 513 pages
...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 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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Dialogues on the First Principles of the Newtonian System, Volume 4

Walter Henry Burton - Astronomy - 1828 - 84 pages
...hand, equal triangles Prop. xii. upon the same base (or upon equal bases in the same straight line) and upon the same side of it, are between the same parallels. For if the straight line which joins the vertices of the two triangles be not parallel to the base,...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...in the circumference which bisectsthe angle between them.] (c) The vertices of all equal spherical triangles upon the same base and upon the same side of it, lie in the circumference of a small circle, such that one equal and parallel to it may be drawn through...
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