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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Page 111
by Thomas Perronet Thompson - 1833 - 150 pages
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 pages
...The diagonals of a parallelogram bisect each other. PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. .. Let the parallelograms ABCD, EBCFbe on the '• same base BC, and between the same parallels AF, BC: the parallelogram...
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874 - 130 pages
...to a given straight line of unlimited length from a given point without it. 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. If a straight line be bisected, and produced to any point, the rectangle contained by the whole...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...two equal parts. Therefore, the opposite sides, &c. QED Proposition 35. — Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the same parallels AF, BC; The parallelogram...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 446 pages
...of the one shall be equal to the angle contained by the two sides, equal to them, of the other. 2. Triangles upon the same base, and between the same parallels, are equal to one another. 3. If the square described upon one of the sides of a triangle be equal to the squares described upon...
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Inventional Geometry: A Series of Problems, Intended to Familiarize the ...

William George Spencer - Geometry - 1876 - 118 pages
...make two triangles that shall be equal to each other, and yet not similar ? 137. Can you show that all triangles upon the same base and between the same parallels are equal to one another 'i 138. Can you place a circle, whose radius is 1J inch, so that its circumference may touch two points...
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876 - 784 pages
...equal to two right angles, the two straight lines shall be parallel to one another. 8. Parallelograms upon the same base, and between the same parallels, are equal to one another. Are the parallelograms equal in all respects ? 1. Simplify 1 — | -j 1 — *-(*— ) >• , and...
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Examination Christmas,1875

Education Department,London - 1876 - 1010 pages
...? Construct the triangle when each side is equal to half the sum of the other two. SECTION III. 2. Triangles upon the same base and between the same parallels are equal. A line drawn through the middle points of the sides of a triangle is parallel to the base. 3. In any...
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A graduated course of problems in practical plane and solid geometry

James Martin (of the Wedgwood inst, Burslem.) - 1876 - 334 pages
...on the following problems he should thoroughly master the subjoined theorems.) (A.) "Parallelograms upon the same base, and between the same parallels, are equal to each other" (in area). — Euc. I., 35. Ex. ABCD, DBCF— NOTE 1. — " Between the same parallels...
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The Teachers' assistant and pupil teachers' guide, Volume 1

1876 - 400 pages
...equal to two right angles. What ratio does the angle of a regular hexagon bear to a rig] it angle? 2. Triangles upon the same base and between the same parallels are equal. A line drawn through the middle points of the sides of the triangle is parallel to the base. 3. In...
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The Madras University Calendar, Volume 1

University of Madras - 1876 - 580 pages
...D. Prove that the exterior angle ACD is greater than the angle ABC. III. Prove that triangles on the same base and between the same parallels are equal to one another. (a) Two equal triangles have two sides of the one equal to two sides of the other. What con elusion...
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