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" Any two sides of a triangle are together greater than the third side. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 30
av Robert Simson - 1806 - 518 sider
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The Geometrical Companion: In which the Elements of Abstract Geometry are ...

George Darley - 1828 - 169 sider
...the side which the sparrow has to fly in proportion to that which it has to fly itself. ART. 43. " Any two sides of a triangle are together greater than the third sidr." As I have observed before, we often, without knowing an angle from a triangle, give an involuntary...
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Elements of the Geometry of Planes and Solids: With Four Plates

Ferdinand Rudolph Hassler - 1828 - 159 sider
...neither equal nor less than AB, it must be greater than it; as was to be demonstrated. § 19. THEOREM. Two sides of a triangle are together greater than the third side. APPLIC. Let ABC, (fig. 26.) be a triangle, the two sides AC, and CB, taken together, are greater than...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 sider
...AB; therefore AC is greater than AB. Wherefore, the greater angle &c. QED PROPOSITION XX. THEOREM. Any two sides of a triangle are together greater than...third side. Let ABC be a triangle; any two sides of it are together greater than the third side, namely, the sides BA, AC are greater than the side BC ; and...
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Self-examinations in Euclid

John Martin Frederick Wright - 1829 - 188 sider
...right angles; .-. angles A, ABC are together < than two right angles. PROP. XX. 56. To prove that ' any two sides of a triangle are together greater than the third side,' what is the general construction ? From the point where they meet, produce either of the two sides...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...not the case. Therefore AB cannot but be greater than A C. Therefore, &c. PROP. 1 0. (Eue. i. 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let А В С be a triangle...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 sider
...equal to AB; therefore AC is greater than AB. Wherefore the greater angle, &c. QE D PROP. XX. THEOR. I Any two sides of a triangle are together greater than...side, viz. the sides BA, AC greater than the side BC j and AB, BC greater than AC; andBC, CA greater than AB. Produce BA to the point D, and make (3. 1.)...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 sider
...BE, EC. But AE, EC are equal to AC; therefore BA, AC are together greater than BE, EC. Again, because two sides of a triangle are together greater than the third side, EC and ED are together greater than CD. To each of these add DB; therefore EC, ED, DB are together...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...is not the case. Therefore AB cannot but be greater than A C. Therefore, &c. PROP. 10. (Eue. L 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let А В С be a triangle...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...angle of every triangle is subtended by the greater side, or has the greater side opposite to it. XX. Any two sides of a triangle are together greater than the third side. XXI. If from the ends of one side of a triangle, there be drawn two straight lines to a point within...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 sider
...than BAC, by preceding ART. ; which it is not. Hence BA must be greater than BC. This, &c. ART. 43. Any two sides of a triangle are together greater than the third tide. In the triangle ABC, any two of its sides, as AB, BC, are together greater than the third side...
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