 CA' and C'A in B 19 AB' and A'B in C 19 then the triangle A 1 B 1 C 1 will be in perspective with each of the given triangles, and the three triangles will have a common axis of perspective. » 5. When three triangles are in perspective two by two and...  An Elementary Treatise on Modern Pure Geometry - Page 104by Robert Lachlan - 1893 - 288 pagesFull view - About this book
 | John Casey - Geometry - 1882 - 186 pages
...centre and the axis of perspective. Prop. 13.— When three triangles are two by two in perspective, and have the same axis of perspective, their three centres of perspective are collinear. Let abe, a'b'c', a"i"c"be the three As whose corresponding sides are concurrent in the collinear points... | |
 | William John M'Clelland - 1886 - 210 pages
...been mastered (see Casey's Sequel, Book VI.). (1) When three triangles are tiro by two in perspective, and have the same axis of perspective, their three centres of perspective are concyclic. (2) When three triangles are two by two in perspective, and have the, same centre of perspective,... | |
 | John Casey - Geometry - 1886 - 262 pages
...centre and the axis of perspective. Prop. 13. — When three triangles are two ly two in perspective, and have the same axis of perspective, their three centres of perspective are eottinear. Let ale, afb'c', a"i"c"be the three As -whose corresponding sides are concurrent in the... | |
 | John Casey - Geometry - 1888 - 279 pages
...centre and the axis of perspective. Prop. 13. — When three triangles are two by two in perspective, and have the same axis of perspective, their three centres of perspective are collinear. Let abe, ofb' cf, #"5'V'be the three As whose corresponding sides are concurrent in the collinear points... | |
 | John Casey - Geometry - 1895 - 216 pages
...centre and the axis of perspective. Prop. 13. — When three triangles are two by two in perspective, and have the same axis of perspective, their three centres of perspective are eolUnear. Let ale, a'l'e', a" I" c" be the three As whose corresponding sides are concurrent in the... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...line. But these intersections are the centres of perspective of tne original triangles. 67. Cor. — If three triangles are in perspective two by two and have the same axis of perspective, the three triangles formed by joining the corresponding vertices of these triangles are also in perspective... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...straight line, the lines joining the corresponding vertices of the triangles meet in a point. § 65 3. If three triangles are in perspective two by two and have the same centre of perspective, their three axes of perspective meet in a point. § 68 spending vertices of... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...of either system of triangles passes through the centres of perspective of the other system. 68. If three triangles are in perspective two by two and have the same centre of perspective, their three axes of perspective meet in a point. Hint. — Let ABC, A'B'C',... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1898 - 324 pages
...corresponding sides of the triangles intersect in points which are in a straight line. § 62 3. If three triangles are in perspective two by two and have the same axis 1. Two points determine a straight line. 2. If the points of intersection of the corresponding sides... | |
 | Edward Harrison Askwith - Conic sections - 1917 - 302 pages
...each of the given triangles, and the three triangles will have a common axis of perspective. » 5. When three triangles are in perspective two by two...their three centres of perspective are collinear. 6. The points Q and E lie on the straight line AC, and the point V on the straight line AD - VQ meets... | |
| |
