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If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 94
by Euclid, James Thomson - 1837 - 390 pages
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814
...at D,) and the angles AlJD, CAD equal ', and also the side AD common; these triangles therefore have two angles of the one equal to two angles of the other, each to each, but the common side AD not lying either between given, or opposite equal angles, the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...BD, and that the right angle BED is equal to the right angle BFD, the two triangles • EBD, FED have two angles of the one equal to two angles of the other, and the side BD, which is opposite to one of the equal angles in each, is common to both ; therefore their...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...then, (IX.) . sin S s\n A sin «S'sin A .s\nS"s\nA" (235.) COR. 2. If two spherical triangles have two angles of the one equal to two angles of the other, each to each, or an angle of the one being equal to an angle of the other, if two other angles, one...
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Encyclopaedia Perthensis; or, Universal dictionary of Knowledge ..., Volume 10

Encyclopaedia Perthensis - 1816
...Any two angles of a triangle are together lefi than two right angles. COR. 3. If two triangles have two angles of the one equal to two angles of the other, the remaining angle of the one is equal to the remaining angle of the other. Coa. 4. The two acute...
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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volume 10

...Any two angles of a triangle are together lefs than two right angles. COR. 3. If two triangles have two angles of the one equal to two angles of the other, the remaining angle of the one is equal to the remaining angle of the other, COR. 4. The two acute...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...vertex to the base, bisecting the vertical angle. PROP. XXXII. . • (xxvi.) If two triangles have two angles of the one equal to two angles of the other, the third angle of the one shall also be equal to the third angle of the other. (XXVII.) The angle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...than the angle EDF. Wherefore, if tw» triangles, &c. QED PROP. XXVI. THEOR. If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal angles,...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 596 pages
...parallel to CD, the alternate angles, GFE, FGH, are also equal; therefore the two triangles GEF, FHG, have two angles of the one equal to two angles of the other, each to each ; and the side FG, adjacent to the equal angles, common ; the triangles are therefore...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...takes place when in each triangle two sides respectively equal, form an equal angle ; and also when two angles of the one, equal to two angles of the other, are formed on an equal side. It is easy to demonstrate these propositions in the same manner as in...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...equal to KCF, and the right angle FHC equal to the right angle FKC; therefore in the triangles FHC, FKC there are two angles of the one equal to two angles of the other, each to each ; and the side FC, which is opposite to one of the equal angles in each, is common to...
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