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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. either the sides adjacent to the equal... "
A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ... - Page 53
by Daniel Cresswell - 1816 - 294 pages
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...like may be proved in all other triangles under the same conditions. Wherefore, universally, if two triangles have two angles of the one, equal to two angles of the other respectively ; &c. Which was to be demonstrated. PROPOSITION XXVII. THEOREM. — If a straight line...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...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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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...by BD, and because the right angle BED is equal to the right angle BFD, the two triangles EBD, FBD 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...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...equal to KCF, and the right angle FHC equal to the right angle FKC; in the triangles FHC, FKC there are two angles of the one equal to two angles of the other, and the side FC, which is opposite to one of the equal angles in each, is common to both : therefore...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...the greater base, shall be greater than the angle contained by the sides of the other. XXVI. If two triangles have two angles of the one equal to two...other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal angles, or the sides opposite to the equal angles in each;...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...bisected by BD, and that the right angle BED is equal to the right angle BFD, the two Iriangles EBD, FBD 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...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 246 pages
...and the triangle bdc must coincide with the triangle abc, and be equal to it. M. — Hence, if two triangles have two angles of the one equal to two angles of the other, each to each, and have likewise one side equal to one side, how must these sides be situated in order that the triangles...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...be > Z EOF. PROPOSITION XXVI. (Argument ad absurdum). Theorem. If two triangles have two angles of 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, or opposite to the equal angles in each : then...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 254 pages
...if the equal angles be subtracted from these equals, the remaining angles must be equal. M.—If two triangles have two angles of the one equal to two angles of the other, each to each, what may be said of the remaining third angles ? P.—They must be equal,—for the reason alleged...
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