 | Oxford univ, local exams - 1885 - 358 pages
...proves that the parallelograms about the diameter of a square are likewise squares. 5. Equal triangles on the same base, and on the same side of it, are between the same parallels. 6. If a straight line be bisected, and produced to any point, the square on the whole line thus produced,... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...equal to half the trapezium. PEOP. XXXIX.— THEOREM. Equal triangles (BAC, BDC) on the same bose (BC) and on the same side of it are between the same parallels. Dem. — Join AD. Then if AD be not parallel to BC, let AE be parallel to it, and let it cut BD in... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...same base. CONCLUSION. AB + AC < A'B + A'C. PROOF. A A' || BC. (253. INVERSE. Equivalent triangles on the same base, and on the same side of it, are between the same parallels.) Draw CND ± A A', meeting BA produced in D. Join A'D. 4NAC = £ACB, (168. If a transversal cuts two... | |
 | Law - 1889 - 896 pages
...Through a given point draw a right line parallel to a given right line. 4. Prove that equal triangles on the same base and on the same side of it are between the same parallels. 5. The sum of the four angles of any quadrilateral is equal to four right angles. 6. Prove that the... | |
 | Euclid - Geometry - 1890 - 442 pages
...CDQ = half O CDYQ; /. A ABP = A CDQ. Proposition 39. THEOREM — Triangles of equal area, which are on the same base, and on the same side of it, are between the same parallels. Let AS PAB, QAB be equal in area, and on the same side of same base AB. Assume that the || to AB, through... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...triangle equivalent to a given rectilineal figure. (Syllabus.) PROPOSITION 39. THEOREM. Equal triangles on the same base and on the same side of it are between the same parallels. Let ABC and DBC be equal As on the same base BC, and on the same side of it, they shall be between... | |
 | Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...Triangles on equal bases and between the same parallels are equal to one another. 39. Equal triangles on the same base and on the same side of it are between the same parallels. 40. Equal triangles on equal bases in the same straight line and on the same side of it are between... | |
 | Queensland. Department of Public Instruction - Education - 1892 - 508 pages
...if any one of the three given lines is not less that the sum of the other two. 20 5. Equal triangles on the same base and on the same side of it are between the same parallels. 22 G. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles... | |
 | Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 188 pages
...bisected by the base, their areas are equal. 139 Proposition 39. 141. Triangles of equal area which are on the same base and on the same side of it, are between the same parallels. Let ABC, DBC represent triangles upon the same base BC and on the same side of it, and let the area... | |
 | Euclid - Geometry - 1892 - 460 pages
...see page 73.] PROPOSITION 40. .THEOREM. Equal triangles, on equal bases in the same straight line, and on the same side of it, are between the same parallels. Let the triangles ABC, DEF which stand on equal bases BC, EF, in the same straight line BF, and on... | |
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DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. 
