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" PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... "
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 36
by Euclid, James Thomson - 1837 - 390 pages
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 192 pages
...the parallelogram ABCD shall be equal to the parallelogram EBCF. * EUCLID'S enunciation of this is ' Parallelograms upon the same base and between the same parallels are equal to one another'. By 4 base' is meant the side on which the parallelogram may be supposed to stand; and ' between the...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...? The line joining the bisections of two sides of a triangle is parallel to the base. 3. Triangles upon the same base, and between the same parallels are equal to one another. The lines joining the bisections of the sides of any quadrilateral figure, together constitute a parallelogram....
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855
...equal, each to each, namely, those to which the equal sides are opposite, 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. In any triangle, if the square of one of the sides is equal to the squares of the two other sides,...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...reduce it, by degrees, to an equivalent triangle. PROP. XXXVIII. THEOREM. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABС, DEF, he upon equal bases B С, EF, and between the same parallels BF, 'A D. The triangle...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...to the parallelogram EHGF ; wherefore EHGF is also equal to ABC D. XXXIX.— EUCLID I. 37. Triangles upon the same base and between the same parallels are equal to one another. Let the triangles ABC, DBC (Fig. 31) be upon the same base BC, and between the same parallels AD, BC ; the...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...Emmanuel College. WILLIAM HENRY BESAHT, MA St John's College. TUESDAY, January 6, 1857. 9... 12. 1. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. ABC is an isosceles triangle, of which A is the vertex : AB, AC, are bisected in D and E respectively...
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A course of practical geometry for mechanics

William Pease - 1856
...opposite the base, to meet these perpendiculars, and the required rectangle will be formed. REASON : " Parallelograms, upon the same base, and between the same parallels," are equal to each other. (Euclid, Book I. Prop. 35.) PROBLEM LXX. To make a rectangle, one of its sides being given,...
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Manual of Method for the use of teachers in elementary schools

W. F. RICHARDS - Education, Primary - 1856 - 184 pages
...are equal, and if the equal sides be produced, the angles at the other side of the base are equal. 2. Parallelograms upon the same base and between the same parallels are equal. 3. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and...
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National Society's Monthly Paper

1856
...angles at the other side of the base are equal. ce, te anges at te oter se of te base are equa. 2. Parallelograms upon the same base and between the same parallels are equal. 3. To a given straight line to apply a parallelogram which shall be equal to a given triangle, ve one...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 12 pages
...triangle be produced, the exterior angle is greater than either of the interior opposite angles. 2. Parallelograms upon the same base and between the same parallels are equal to one another. VOLUNTARY PORTION. 1. The opposite angles of a quadrilateral figure, inscribed in a circle, are together...
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