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" If from any point within a triangle, two straight lines be drawn to the extremities of either side, their sum will be less than Hie sum of the two other sides of the triangle. "
Exercises on the geometry and measurement of plane figures, being solutions ... - Página 9
por Richard Wormell - 1883 - 192 páginas
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1828 - 346 páginas
...shortest distance from B to C ; therefore, BC is less than BA+AC. •-- THEOREM. $ 41. If , from any point within a triangle two straight lines be drawn to the extremities of either side, the sum of these straight lines will be less than that of the two other sides of the triangle....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 394 páginas
...points A and 15 (Def. 3.) ; hence AC + CB is greater than AB. A. PROPOSITION VIII. THEOREM. If from any point within a triangle, two straight lines be drawn to the extremities of either side, their sum will be less than Hie sum of the two other sides of the triangle. Let any point,...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 páginas
...of these take AC; then (I. ax. 5.) BA is greater than the excess of BC above AC. PROP. XXI. THEOR. f IF from a point within a triangle, two straight lines be drawn to the extremities of one of the sides, these lines are together less than the other sides, but contain a greater angle....
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - 1844 - 268 páginas
...extremities of the side AB, or AC, it may be proved that AO+BO<AC + BC; and AO+CO<AB+BC. Hence, If from any point within a triangle, two straight lines be drawn to the extremities of either side, the sum of these two lines will be less than the sum of the other two sides of the triangle....
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 páginas
...these take AC ; then (I. ax. 5) BA is greater than the excess of BC above AC. PROP. XXI. THEOB.* — If from a point within a triangle. two straight lines be drawn to the extremities of one of the sides, these lines are together less than the other sides, but contain a greater angle....
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 372 páginas
...its sides, as AC, CB, be greater than the third side AB. A. PROPOSITION VIII. THEOREM. If from any point within a triangle, two straight lines be drawn to the extremities of either side, their sum will lie less than the sum of the two other sides of the triangle. Let any point,...
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The Elements of Euclid: With Many Additional Propositions ..., Parte1

Euclid - 1853 - 176 páginas
...40, cor. 3. . I. 40, cor. 4. . HYPOTHESES. If a straight line bisects the two sides of a triangle. If from a point within a triangle two straight lines be drawn to the extremities of any side. If three straight lines be drawn through the points of bisection of the three sides of a...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 436 páginas
...between any two sides of a triangle ts less than the third side. PROPOSITION Vm. THEOREM. If from any point within a triangle, two straight lines be drawn to the extremities of either side, their sum will be less than that of the two remaining sides of the triangle. Let 0 be...
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Annual Register of the United States Naval Academy ..., Volúmenes25-32

United States Naval Academy - 1874 - 888 páginas
...ri'ßit angle, and perpendicular, parallelogram, rhomb«*, rhomboid, Irapczoid. Trove that if from any point within a triangle two straight lines be drawn to the extremities of either side, their sum will be less than that of the remaining two sides of the triangle. 2. Prove...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 páginas
...than A С. Therefore the triangles coincide and are equal in all respects. THEOREMS FOR EXERCISE. 14. If from a point within a triangle two straight lines be drawn to the extremities of the base, these straight lines shall be together less than the two sides ot the triangle. 15. Two villages, A...
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