 | Daniel Cresswell - 1817 - 454 σελίδες
...perimeter of which shall be respectively equal to the area and perimeter of a given triangle. v (LXIV.) The two triangles formed by drawing straight lines,...point within a parallelogram, to the extremities of either pair of opposite sides, are, together, half of the parallelogram. (LXV.) If two sides of a trapezium... | |
 | Miles Bland - 1819 - 442 σελίδες
...diameter is a mean proportional between the segments intercepted between the diameter and the sides. 7. The two triangles, formed by drawing straight lines...opposite sides, are together half of the parallelogram. 8. If a straight line be drawn parallel to one of the sides of a parallelogram, and one extremity of... | |
 | Edward Riddle - 1824 - 572 σελίδες
...20. The three straight lines which bisect the three angles of a triangle meet in the same point. 21. The two triangles, formed by drawing straight lines...extremities of two opposite sides, are together, half the parallelogram. 22. The figure formed by joining the points of bisection of the sides of a trapezium,... | |
 | Daniel Cresswell - 1825 - 616 σελίδες
...(E. xxxiv. l.) GH=DC=DB, .-. DC+GH=BD+DC=BC; .-. DG+ GH+HC+CD = BA+AC+CB. PROP. LXVII. 86. THEOREM. The two triangles formed by drawing straight lines,...point within a parallelogram, to the extremities of either pair of opposite sides, are, together, half of the parallelogram. Let E be any point in the... | |
 | Adrien Marie Legendre - 1841 - 288 σελίδες
...and BEC=CED. (170.) Q. XL VIII. The two triangles formed by drawing straight lines from any Fig. 338. point within a parallelogram to the extremities of...within the parallelogram ABCD, from which let lines PA, PB, PC, PD, be drawn to the extremities of the opposite sides ; the triangles PAD,PBC, are equal to... | |
 | Euclides - 1846 - 292 σελίδες
...its area will be greatest when they contain a right angle. 93. The two triangles, formed by drawing lines from any point within a parallelogram to the...extremities of two opposite sides, are together half the parallelogram. 94. If from the ends of one of the oblique sides of a trapezium two lines be drawn... | |
 | Euclides - 1847 - 128 σελίδες
...1 altitude. From this Proposition the following are deductions : — PROP. W. THEOR. GEN. ENUN. — The two triangles formed by drawing straight lines...the extremities of two opposite sides, are together equal to half the parallelogram. PART. ENUN. — Let ABCD be a P m, and E any pt. within it. Draw EA,... | |
 | Euclid, Thomas Tate - 1849 - 120 σελίδες
...joins the points of bisection of any two sides of a triangle is equal to half the remaining side. 17. The two triangles formed by drawing straight lines,...point within a parallelogram, to the extremities of 16. The diameters of any parallelogram divide it into four equal triangles. either pair of opposite... | |
 | Euclides - 1852 - 152 σελίδες
...opposite sides or opposite angles of a quadrilateral figure be equal, the figure will be a parallelogram. The two triangles, formed by drawing straight lines...opposite sides, are together half of the parallelogram. If two sides of a trapezium be parallel, its area is equal to half that of a parallelogram whose base... | |
 | Royal college of surgeons of England - 1860 - 332 σελίδες
...described upon the other two sides of it, the angle contained by these two sides is a right angle. 9. The two triangles, formed by drawing straight lines...the extremities of two opposite sides, are together equal to half the parallelogram. PBELIMINAKY GENERAL EXAMINATION. Midsummer, 1868. WEDNESDAY, June... | |
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If from a point, without a parallelogram, there be drawn two straight lines to the extremities of the two opposite sides, between which, when produced, the point does not lie, the difference of the triangles thus formed is equal to half the parallelogram.... 
