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" 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 than the other two sides of the triangle, but shall contain a greater angle. Let... "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 26
by Robert Simson - 1806 - 518 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 333 pages
...Therefore any two sides, &c. QED PROP. XXI. THEOR. If from the ends of one side of a triangle, tJiere 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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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...is impossible ; and, 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...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 ...

Mathematics - 1836 - 472 pages
...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 471 pages
...point within the triangle, these two lines shall be less than the other two sides of the triangle, biit shall contain a greater angle. Let the two straight lines BD, CD be drawn from B, <I, the ends of the side BC of the triangle ABC, to the point D within it ; BD and DC are less than...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...that similarly each of the other pairs of sides is > the remaining side. PROPOSITION XXI. Theorem. If from the ends of the side of a triangle there be...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 - Euclid's Elements - 1837 - 240 pages
...that the sides AB, BC, are greater than CA, and BC, CA, greater than AB. PROPOSITION XXI. THEOREM. If from the ends of the side of a triangle, there...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 - Geometry - 1837 - 318 pages
...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
...lew than the third Mr.." 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...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 - Geometry - 1841 - 351 pages
...are greater than CA, and 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 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
...are greater than CA, and 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...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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