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" If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. "
The Elements of Euclid, the parts read in the University of Cambridge [book ... - Side 22
av Euclides - 1846
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...than AB. Therefore, any two sides, &c. QED PROPOSITION XXI. See N. THEOR. — If from the ends of the side of a triangle, there be drawn two straight lines...the triangle, but shall contain a greater angle. Let ABC be a triangle, and from the points B, C, the ends of the side BC, let the two straight lines BD,...
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The Element of Geometry

John Playfair - 1836 - 114 sider
...therefore, ACB is not a right angle. Therefore, From, &c. QED PROP. XII. THEOR. If from the ends of the side of a triangle there be drawn two straight lines...be less than the other two sides of the triangle. Let the two straight lines BD, CD be drawn from B, C, the ends of the side BC of the triangle ABC,...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...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 the triangle, these two lines shall be less than the other two sides of the triangle, but shall contain a greater angle....
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...the other pairs of sides is > the remaining side. PROPOSITION XXI. Theorem. If from the ends of the side of a triangle there be drawn two straight lines...of the triangle, but shall contain a greater angle. • Steps of the Demonstration. 1. Prove that BA + AC > BE + EC, 2. that BE + EC > CD + DB, 3. that...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...are greater than CA, and BC, CA, greater than AB. PROPOSITION XXI. THEOREM. If from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these two lines shall he less than the other two sides of the triangle, but shall contain a greater angle....
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...than CA, and BC, CA greater than AB. SCHOLIUM. 23 E PROP. XXI. THEOR. If from, the ends of one si'le of a triangle, there be drawn two straight lines to a point within the triangle, these two lines shall be less than the other two sides of the triangle, but shall contain a greater angle....
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...and reason as follows: " For, since BA and AC are together PROP. XXI. THEOR. If from the ends of the side of a triangle there be drawn two straight lines...to a point within the triangle, these shall be less man the other two sides of the triangle, but shall contain a greater angle. Let ABC be a triangle,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...BC, CA greater than AB. Therefore any two sides, &c. UED PROP. XXI. THEOR. If from the ends of the side of a triangle, there be drawn two straight lines...be less than the other two sides of the triangle, out shall contain a greater angle. Let ABC be a triangle, and from the points B, C, the ends of the...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...вc, CA greater than AB. Therefore any two sides, &c. QED PROP. XXI. THEOR. IF from the ends of the side of a triangle there be drawn two straight lines...within the triangle, these shall be less than the two other sides of the triangle, but shall contain a greater angle. Let the two straight lines BD,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...from B to C ; therefore BC is less than BA+AC or BA+AC>BC. PROP. XXI. THEOR. If from the ends of one side of a triangle, there be drawn two straight lines to a point within the triangle, these two lines shall be less than the other two sides of the triangle, but shall contain a greater angle....
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