 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...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 - Euclid's Elements - 1819 - 444 pages
...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... | |
 | Miles Bland - Geometry - 1821 - 898 pages
...opposite side in G, and A " bl AD produced in E ; BF is a mean proportional between FG and FE. Draw Dti parallel to BF, and .-. equal to it ; .-. also AH=...the parallelogram ; as also the triangles APB, DPC. of ABCD. In the same manner if a line be drawn through P parallel to AB or DC, it may be shewn that... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...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 - Euclid's Elements - 1825 - 616 pages
...(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... | |
 | Miles Bland - Euclid's Elements - 1827 - 462 pages
...parallelogram ABCD, let any line BE be drawn cutting the diameter AC in F, the opposite side in G, and AD produced in E ; BF is a mean proportional between...the parallelogram ; as also the triangles APB, DPC. of ABCD. In the same manner if a line be drawn through P parallel to AB or DC, it may be shewn that... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...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 pages
...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 pages
...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 pages
...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... | |
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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.... 
