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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 first six books of the Elements of Euclid, with numerous exercises - Seite 15
von Euclides - 1853 - 147 Seiten
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 516 Seiten
....Therefore any two sides, &c. QED PROP. XXI. THEOR. TF, from the ends of the side of a triangle, there he drawn two straight lines to a point within the triangle,...contain a greater angle.* Let the two straight lines BD, CD be drawn from B, C, the ends of the side BC of the triangle ABC, to the point D within it ; BD and...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 Seiten
...thoy did, there would be two of its sides together not greater than the third. THEOREM — If from the ends of the side of a triangle, there be drawn two straight lines to a point milhin the triangle, these See Note *hall together be less than the two sides of thejirst triangle,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 Seiten
...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 Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...CA greater 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...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 Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 Seiten
...of a triangle there be Sec N. drawn two straight lines to a point within the triangle, these sliall be less than the other two sides of the triangle,...contain a greater angle. Let the two straight lines BD, CD be drawn from B, C, the ends of the side BC of the triangle ABC to the point D within it ; BD and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 Seiten
...of a triangle there be See N. drawn two straight lines to a point within the triangle, these sJiall be less than the other two sides of the triangle,...contain a greater angle. Let the two straight lines BD, CD be drawn from B, C, the ends of the side BC of the triangle ABC to the point D within it ; BD and...
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The Element of Geometry

John Playfair - 1836 - 114 Seiten
...; 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 drawn two...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 Seiten
...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 Seiten
...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 drawn two...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 Seiten
...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 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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