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Books Books 1 - 10 of 45 on If from a point, without a parallelogram, there be drawn two straight lines to the....  
" 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.... "
Geometrical problems deducible from the first six books of Euclid: arranged ... - Page 123
by Miles Bland - 1819 - 377 pages
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An elementary treatise on the geometrical and algebraical investigation of ...

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...
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Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

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...
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A treatise on navigation, and nautical astronomy

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,...
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A supplement to the elements of Euclid

Daniel Cresswell - Mathematics - 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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

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...
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Elements of geometry

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...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

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...
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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 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,...
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The first three books of Euclid's Elements of geometry, with theorems and ...

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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