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" If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. "
The Elements of Euclid, containing the first six books, with a selection of ... - Σελίδα 23
των Euclides - 1874
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...angle EBC: and the angle AEG is •15.1. equal* to the angle BEH: therefore the triangles AEG, BEH have two angles of the one equal to two angles of the other, each to each, and the sides AE, EB, adjacent to the equal angles, equal to one another: • 26. 1. wherefore they have...

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...opposite angle CBF, — Euclid, Book I., Prop. 29. And, since the two triangles AFD and FBC have, thus, two angles of the one equal to two angles of the other, viz., the angle AFD to the angle FBC, and the angle FAD to the angle BFC, and the side AF of the one...

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...mO' and M'N'O' are equal. The angle N'O'M' is common to the two triangles nmO' and N'M'O'; and having two angles of the one equal to two angles of the other, the other angles must be equal, that is, the angle O'M'N' is equal to the angle O' nm ; and this intersection...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

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...together equal to the angles А С D, ACB, that is, to two right angles (2.). Therefore, &c. Cor. 1. If two triangles have two angles of the one equal to two angles of the other, their third angles will likewise be equal to one another. Cor. 2. (Eue. i. 2G, second part of.) Hence,...

Elements of Geometry: Containing the First Six Books of Euclid : with a ...

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...angle BAG is greater than the angle EDF. Wherefore, if two triangles, &c. QED PROP. XXVI. THEOR. I/ two triangles have two angles of the one equal to two angles of the other, each to each; undone side equal lo one side, viz. either the sides adjacent to the equa tangles, or the sides opposite...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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...the angle BAC is greater than the angle EDF. Wherefore, if two triangles, &c. QED PROP. XXVI. THEOR. If two triangles have two angles of the one equal...; and one side equal to one side, viz. either the side adjacent to the equal angles, or the sides opposite to the equal angles in each ; then shall the...

The Moral Class Book, Or The Law of Morals: Derived from the Created ...

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...it. It is a truth, for example, but not a self-evident one, that if one draw two triangles, having two angles of the one equal to two angles of the other,...each ; and one side equal to one side, viz. either of the sides adjacent to the equal angles, or the sides opposite to the equal angles in each; then...

Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

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...universally, if two triangles have two sides of the one, &c. Which was to be demonstrated. PROPOSITION XXVI. THEOREM. — If two triangles have two angles of the one, equal to two angles of the other respectively ; and have moreover one side of the one triangle equal to one side of the other triangle,...

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...angle EEC : and the angle AEG is equal * to the angle BEH ; * 15' l• therefore the triangles AEG, BEH have two angles of the one, equal to two angles of the other, each to each, and the sides AE, EB, adjacent to the equal angles, equal to one another ; wherefore they have their other...

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...together equal to the angles А С D, ACB, that is, to two right angles (2.). Therefore, &c. Cor. 1. If two triangles have two angles of the one equal to two angles of the other, their third angles will likewise be equal to one another. Cor. 1. (Eue. i. 26, second part of.) Hence,...




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