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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. "
Senate Documents, Otherwise Publ. as Public Documents and Executive ... - Side 296
av United States. Congress. Senate - 1880
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 sider
...triangle. For if 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 sider
...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 - 1836 - 114 sider
...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...straight lines to a point within the triangle, these shall be less than the other two sides of the triangle. Let the two straight lines BD, CD be drawn...
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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
...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...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. • Steps...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...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 - 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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The Elements of Euclid

Euclid - 1838 - 416 sider
...greater than CA, and BC, CA greater than AB. Therefore any two sides, &c. Q,. ED PROP. XXI. THEOR. IF, from the ends of the side of a triangle, there...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...
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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...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...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...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...straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, out shall contain a greater angle. Let ABC...
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