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" Equal triangles on the same base, and on the same side of it, are between the same parallels. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 47
by Euclid, Rev. John Allen - 1822 - 494 pages
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Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 96 pages
...half Q EH, .-. A ABC = A DEF (Ax. 7). QED HU TYTv PROP. 39. THEOK. Equal triangles on the same base and on the same side of it are between the same parallels. Given A ABC = A DBC, on same AD base BC. To prove AD || BC. If AD is not || BC, through A draw AE ||...
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The Practical Teacher, Volume 3

Education - 1884
...BA=BE, but BE = AC. Л the triangle ABC is isosceles. Q- b- 2. Equal triangles upon the same base and on the same side of it are between the same parallels. Prop. 39, Bk. I. 3. To a given straight line to apply a parallelogram, which shall be equal to a given...
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884
...same side of it are between the same parallels. GIVEN that the triangles A BC and DBC are equal, and on the same base BC and on the same side of it, and that AD is joined ; IT is REQUIRED TO PROVE that AD is parallel to BC, From A draw AE parallel...
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volume 1

Euclides - 1884
...two sides of the quadrilateral are parallel to one another. (10) 10. Equal triangles on the same base and on the same side of it are between the same parallels. If a quadrilateral is divided into four equal triangles by its diagonals, show that it is a parallelogram....
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...Prove the proposition for the case when the points D and E coincide. 2. Equal ||m8 on the same base and on the same side of it are between the same parallels. 3. If through the vertices of a triangle straight lines be drawn || the opposite sides, and produced...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1885
...DBCF ; and they are equal, since each is double of A DBC. I. 34 2. Let ABCD, EBCF be two equal ||m' on the same base BC, and on the same side of it. If AD, or AD produced, be not in the same straight line with EF, let it cut BE and CF, or these straight...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - Euclid's Elements - 1885 - 312 pages
...is 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...
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Senate Documents, Otherwise Publ. as Public Documents and ..., Volume 3

United States. Congress. Senate - United States - 1880
...invariable. Under what conditions will this difference be /ею :' 2. Equal triangles on the same base, and on the same side of it, are between the same parallels. The sides .11! and .K'of a triangle are bisected in I) and E respectively, and RE, CD are produced...
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University of Oxford. Examination of women. Examination papers

Oxford univ, local exams - 1885
...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,...
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Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885
...are equal to twice as many right angles as the figure has sides. 3. Equal triangles on the same base, and on the same side of it, are between the same parallels. If two equal lines AB, CD cross one another, and А С is equal to BD, then shall AD be parallel to...
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