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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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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...CONCLUSION. AB + AC<A'B + AC. PROOF. AA || BC. (253. INVERSE. Equivalent triangles on the same base, and on the same side of it, are between the same parallels.) Draw CND _L AA \ meeting BA produced in D. Join A'D. 4NAC = 4ACB, (168. If a transversal cuts two parallels,...
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885
...is equal to half the trapezium. PEOP. XXXIX.— THEOREM. Equal triangles (BAC, BDC) on the same Iase (BC) and on the same side of it are between the same parallek. Dem. — Join AD. Then if AD be not parallel to BC> let AE be parallel to it, and let it...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 366 pages
...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...
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The Irish Law Times and Solicitors' Journal, Volume 23

Law - 1889
...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...
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The Laws of Motion: An Elementary Treatise on Dynamics

W. H. Laverty - Dynamics - 1889 - 224 pages
...distances of 9 of the points of division. 40. ABC, DBC are two uniform isosceles triangular laminae on the same base BC and on the same side of it. If the centre of mass of the four-sided figure A BDC is at D ; find the ratio of the areas of the two...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...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 the same parallels. Join AD. AD shall be || to BC. For if it is not, through...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 400 pages
.../. 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...
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - Euclid's Elements - 1891 - 79 pages
...can be drawn to a given straight line from a given point without it. 2. BAC and BDC are two triangles on the same base BC and on the same side of it, and the angle BAG is equal to the angle BDC. Prove that each of the vertices A and D must lie without...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1892
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 518 pages
...and mi the xnnic side of it, ar?, between the same parallels. Let the triangles ABC, DBC which stand on the same base BC, and on the same side of it, be equal in area : then shall they be between the same parallels ; that is, if AD be joined, AD shall...
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