| Daniel Cresswell - Euclid's Elements - 1817 - 436 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 - Geometry - 1819 - 377 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 - 438 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 - 1824
...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 - 582 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 - Geometry - 1827 - 377 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 - Mathematics - 1841 - 235 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
...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... | |
| William Trollope - 1847
...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,... | |
| Euclides - 1849
...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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