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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 - Σελίδα 15
των Euclides - 1853 - 147 σελίδες
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...greater than AB. Wherefore any two sides, &c. QED 59. PROPOSITION XXI. — THEOREM. 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 two sides of the triangle, but shall contain a greater angle. Let ABC be a triangle, and D a point...

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...semi-perimeter is less, than the sum of the three medians. PROPOSITION 21. THEOREM. If from the ends of any side of a triangle there be drawn two straight lines to a point within the triangle, these straight lines shall be together less than the other two sides of the triangle, but shall contain a...

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...that there are several ways in which the line may be drawn. Prop. 2, Bk. I. 2. If from the ends of a side of a triangle there be drawn two straight lines...other two sides of the triangle, but shall contain я greater angle. Prop. 21, Bk. I. 3. Show that the vertex of an isosceles triangle and the intersections...

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...(2) are not to be worked by male candidates. II. [15] GEOMETRY. Time, 1 luour 30 min. ]. It from the ends of the side of a triangle, there be drawn two...straight lines to a point within the triangle ; these will be together less than the other sides of the triangle, but will contain a greater angle. -. If...

Senate Documents, Otherwise Publ. as Public Documents and Executive ..., Τόμος 3

...parts is it possible, by mean« of Euclid's constructions, to divide a right angle t 'i- If from the ends of the side of a triangle there be drawn two...straight lines to a point within the triangle, these straight lines shall be less than the other two sides of thr triangle. A triangle and a quadrilateral,...

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...5 ; 4. Find their scores. GEOMETRY. (Exhibitions and Bursaries.} TIME : THREE HOURS. 1. If from the ends of the side of a triangle, there be drawn two...of the triangle, but shall contain a greater angle. 2. Assuming the construction of the 47th proposition of the First Book of Euclid ; analyze the proof...

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...two.thirds of the sum of the three diagonals AD, BE, CF. PROPOSITION 21. THEOREM. If from the ends of a side of a triangle there be drawn two straight lines...of the triangle, but shall contain a greater angle. From the ends B, C of the side BC of the A ABC let the two st. lines BD. CD be drawn to a point D within...

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...Euc. I. 7 where the vertex of each triangle is without the other triangle. 3. If from the ends of a side of a triangle there be drawn two straight lines to a point within the triangle, these shall contain a greater angle than the angle contained by tht> other two sides of the triangle. 4. Give the...

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...opposite it. 20. Any two sides of a triangle are together greater than the third side. 21. If from the ends of the side of a triangle there be drawn two...of the triangle, but shall contain a greater angle. 22. To make a triangle of which the sides shall be equal to three given straight lines, any two of...

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...triangle, there be drawn (wo straight lines to a point within the triangle, then these straight lines shall be less than the other two sides of the triangle, but shall contain a greater angle. A BC Let ABC be a triangle, and from B, C, the ends of the side BC, let the two straight lines BD,...