 | Queensland. Department of Public Instruction - 1911 - 218 páginas
...ratio of the squares on corresponding sides. 4. If two chords of a circle intersect at a point inside the circle, the rectangle contained by the segments...rectangle contained by the segments of the other. 5. Prove that the three altitudes of a triangle are concurrent. U. The sum of the rectangles contained... | |
 | Queensland. Department of Public Instruction - 1912 - 234 páginas
...circle can be described about the quadrilateral. 9. Prove that if two chords of a circle cut one another the rectangle contained by the segments of the one is equal to the rectangle contained by the segment* of the other. Two perpendicular lines AB, CD intersect at O : OA = 2 inches, OB = 9 inches,... | |
 | University of South Africa - 1913 - 768 páginas
...straight line is a tangent to the circle. If two chords of a circle intersect either inside or outside the circle, the rectangle contained by the segments...rectangle contained by the segments of the other. The rectangle contained by the segments of a chord drawn from an external point to a circle is equal... | |
 | 1924 - 544 páginas
...who shall have the courage to put Euclid III 35 // in a circle two straight lines cut one another, the rectangle contained by the segments of the one...the rectangle contained by the segments of the other and Euclid III 36 // a point be taken outside a circle, and from that point there fall on the circle... | |
 | Arthur Warry Siddons, Reginald Thomas Hughes - 1926 - 202 páginas
...(i). If two chords of a circle intersect inside the circle, the rectangle contained by the segments of one is equal to the rectangle contained by the segments of the other*. Data AB and CD are two chords of a circle meeting in P. To prove that PA . PB = PC . PD. Construction... | |
 | Edward Grant - 1974 - 890 páginas
...(New York : Dover, 1956), the second part of Elements 111.35 says that if two lines intersect in a circle "the rectangle contained by the segments of...rectangle contained by the segments of the other" (Heath, II, 71). Therefore, in Fig. 2, ef2 -cf-fp. 6. Elements II. 1 enunciates the geometric equivalent... | |
 | Audun Holme - 2002 - 408 páginas
...ends with the following two propositions: Two Cords If in a circle two straight lines cut one another, the rectangle contained by the segments of the one...rectangle contained by the segments of the other. ab a Fig. 4.2. The large square with side a has area a2, the small one with side 6 has area 62. The... | |
 | Immanuel Kant - 2003 - 626 páginas
...3:413-19). Cf. Euclid, Elements, Book III, Theorem XXXV: 'If in a circle two straight lines cut one another, the rectangle contained by the segments of the one is equal to the rectangle contained by the segment of the other.' Cf. Euclid, Elements, Book III, Theorem XXXVI: 'If a point be taken outside... | |
 | Actuarial Society of America - 1914 - 524 páginas
...sides of a triangle is parallel to the third side. (6) Show that if two chords of a circle intersect within the circle, the rectangle contained by the...rectangle contained by the segments of the other. 15. (a) Two circles touch one another externally at A and through A a straight line is drawn cutting... | |
 | 1965 - 232 páginas
...tangent at C in T. Prove 6-a Theorem 39. // two chords of a circle intersect either inside or outside the circle, the rectangle contained by the segments...rectangle contained by the segments of the other. D C Fig.l. Fig. 2. Given. AB and CD are chords of a circle intersecting at P. Reqd. To prove AP.PB=CP.PD.... | |
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When it is affirmed (for instance) that " if two straight lines in a circle intersect each other, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other... 
