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" If two triangles have two sides of the one equal to two sides of the... "
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... - Page 27
by Charles Davies - 1854 - 432 pages
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Remarks on mathematical or demonstrative reasoning:its connexion with logic ...

Edward Tagart - Logic - 1837 - 156 pages
...question within a certain class, viz. the class of angles subtended by equal bases, in triangles which have two sides of the one equal to two sides of the other, of which equality is demonstrated ia the fourth proposition : and let us remember that every...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 382 pages
...+ OC< BD + DC ; therefore, still more isBO + OC<BA + AC. PROPOSITION IX. THEOREM. If two triangles have two sides of the one equal to two sides of the...angle. Let BAC and EDF be two triangles, having the sideAB=DE, AC =DF, and the angle A>D;thenwillBC> EF. Make the angle CAGB =D; take AG=DE, and draw CG....
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...sufficiently long for this. It must of course be produced. PROP. XXIV. THEOR. If two triangles haee two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained ky the two...
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Hints, Theoretical, Elucidatory, and Practical, for the Use of Teachers of ...

Olinthus Gregory - Euclid's Elements - 1840 - 204 pages
...the two triangles ABC, and ACB, AB is equal to AC, and AC to AB ; therefore, two sides of the one are equal to two sides of the other, each to each ; and the angle BAC is equal to the angle CAB, being in fact one and the same angle ; wherefore, by prop. 4,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...therefore BC is greater than EF. Therefore, if two triangles, &c. QED PROP. XXV. THEOR. If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other; the angle contained by the sides of that...
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Chambers's information for the people, ed. by W. and R. Chambers, Volume 2

Chambers W. and R., ltd - 1842 - 744 pages
...comparison of triangles. This important theorem, as stated by Euclid, is aa follows :— If two triangles have two sides of the one equal to two sides of the other, each to each, and have Uk«win the angles contained by those sides equal to one another, their bases, or third sides,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...the angle FAG is made equal to the given rectilineal angle DCE. PROP. XXIV. THEOR. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of the one greater than the angle contained by the two sides...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...straight line/g' ; therefore (8. 1.) the angle dee is equal to PROP. XXIV. THEOR. IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two...
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Elements of Geometry and Trigonometry

Geometry - 1843 - 376 pages
...+ OC< BD + DC ; therefore, still more isBO + OC<BA + AC. PROPOSITION IX. THEOREM. If two triangles have two sides of the one equal to two sides of the...BAC and EDF be two triangles, having the side AB=DE, AC =DF, and the angle A>D ; then will BC> EF. A 18 triangle GAC is equal to DEF, since, by construction,...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...is a plane rectilineal angle ? When is a straight line said to touch a circle ? 2. If two triangles have two sides of the one equal to two sides of the other, each to each; and have likewise the angles contained by those sides equal to one another; they shall likewise have their...
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