| Henry William Watson - Geometry - 1871 - 285 pages
...proved, take away AB from each, therefore BC is greater than AC~AB. PROPOSITION 2. If from the ends of a **side of a triangle there be drawn two straight lines to a point within the triangle, these** two lines shall be together less than the two remaining sides of the triangle. From B and C the ends... | |
| Robert Johnston (F.R.G.S.) - Civil service - 1872 - 178 pages
...and a rhombus, and give Euclid's 12th axiom (relating to parallel lines). 2. If from the ends of a **side of a triangle there be drawn two straight lines...within the triangle, these shall be less than the** oiher two sides of the triangle, but shall contain a greater angle. 3. What is meant by a corollary... | |
| Student teachers - 1873
...same manner it mny be shown that AB, BC, are greater than CA ; find BC, CA, greater than AB. XXI. — **If from the ends of the side of a triangle, there be drawn** t^vo straight lines to a point within the triangle, these shall be less than the other two sides of... | |
| Robert Johnston (F.R.G.S.) - 1873
...and a rhombus, and give Euclid's 12th axiom (relating to parallel lines). 2. If from the ends of a **side of a triangle there be drawn two straight lines to a point** wilhin the triangle, these shall be less than the other two sides of the triangle, but shall contain... | |
| 1874
...the sides also which subtend, or are opposite to, the equal angles shall be equal to one another. 2. **If from the ends of the side of a triangle there be...of the triangle, but shall contain a greater angle.** 3. If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite... | |
| 1874
...former, which is impossible. Hence it follows that PROPOSITION XVII. If from the ends of one of the sides **of a triangle there be drawn two straight lines to...of the triangle but shall contain a greater angle.** '~D a -# From the ends B, C of the side BC of the &ABC let the two straight lines BD, CD be drawn to... | |
| 1874
...than AC ; and BC, CA greater than AB. Therefore any two sides, <fec. QED Proposition 21. — Theorem. **If from the ends of the side of a triangle there be...triangle, these shall be less than the other two sides of** t/ie triangle, but shall contain a greater angle. Let ABC be a triangle, and from the points B, C,... | |
| thacker, vining, and co. - 1874
...ratio and similar rectilineal figures. 2. If from the ends of a Bide of a triangle there be drawn 6 **two straight lines to a point within the triangle...of the triangle, but shall contain a greater angle.** If two points be taken in the base of a triangle at equal dis- 6 tances from, and on opposite sides... | |
| 1874
...greater than AB. Therefore any two sides, &c. QED Proposition 21. — Theorem. If from the ends of t/ie **side of a triangle there be drawn two straight lines to a point within the triangle, these shall be** las titan the other two sides of the triangle, but shall contain a greater angle. Let ABC be a triangle,... | |
| Charles Mansford - 1874
...quadrilateral are together greater than its two diagonals. PROPOSITION 21. THEOREM. If from the ends of ike **side of a triangle there be drawn two straight lines to a point within the triangle, these** slutll be less than the other two sides of the triangle, but shall contain a greater angle. j Let ABC... | |
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