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" If two triangles have two sides of the one equal to two sides of the... "
The Element of Geometry - Page 1
by John Playfair - 1836 - 114 pages
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...viz., the angle ABC to the angle DEF, b Ax. 8. and the angle ACB to the angle DFE. Therefore, if two triangles have two sides of the one equal to two sides of the other, &c. QED PROPOSITION V. THEOREM.* The angles which are at the base of isosceles triangles are...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...AB, the angle FAG is made equal to the given rectilineal angle DCE. Which was to be done. PROP. XXIV. THEOR. If two triangles have two sides of the one equal to two sides See N. of the other, each to each, but the angle contained by the two sides of one of them greater...
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Dialogues on the First Principles of the Newtonian System, Volume 4

Walter Henry Burton - Astronomy - 1828 - 68 pages
...the proposition is a fundamental one, we will prove it. Suppose two triangles, of whatever form, to have two sides of the one equal to two sides .of the other, each to each; and the angle contained between those two sides in the one triangle to be equal to that which is contained...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 172 pages
...the two triangles would therefore be equal in all their parts. And we say universally, — When two triangles have two sides of the one equal to two sides of the other, each to each, and the angle contained by these two sides of the one, equal to the angle contained by the two sides of...
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Self-examinations in Euclid

John Martin Frederick Wright - Euclid's Elements - 1829 - 188 pages
...considered by Euclid. Of these seven combinations, six of them belong to the case of two triangles, having two sides of the one equal to two. sides of the other, each to each, and one angle to one angle, viz. those to which equal sides are opposite. This case will be fully discussed...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 516 pages
...lines, a part AE has been cut off equal to C the less. Which was to be done. PROP. IV. THEOREM. IF two triangles have two sides of the one equal to two sides of the other, each to eacji ; and have likewise the angles contained by those sides equal to one another, they shall likewise...
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ELEMENTS OF GEOMETRY UPON THE INDUCTIVE METHOD.

JAMES HAYWARD - 1829
...the two triangles would therefore be equal in all their parts. And we say universally,— When two triangles have two sides of the one equal to two sides of the otlicr, each to each, and the angle contained by these two sides of the one, equal to the angle contained...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...less. Which was to be done. PROPOSITION IV. THEOREM. IF two triangles have two sides of one triangle equal to two sides of the other, each to each; and have also the angles contained by those aides equal to each other; their third sides will be equal; and...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...to, or greater than, or Jess than a semicircumference. 190 VI. $ 2.] 191 PROP. 13. If two spherical triangles have two sides of the one equal to two sides of the other, fach to each, and likewise the included angles equal ; their other angles shall be equal, each...
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A System of Plane and Spherical Trigonometry: To which is Added a Treatise ...

Richard Wilson - Logarithms - 1831 - 330 pages
...spherical polygon is less than the circumference of a great circle, (art. 32.) 49. PROP. If two spherical triangles have two sides of the one equal to two sides...angles contained by those sides equal to one another, the two triangles shall be equal. This proposition is proved by precisely the same reasoning as is...
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