Books Books
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

## Papers Read at the Royal Institute of British Architects

Architecture - 1865 - 276 pages
...Given the vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms upon the same base and between the same parallels are equal to one another. Shew this is equally true of triangles. 4. Prop. 44. — Problem. To a given straight line to apply...

## The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...BC divides the parallelogram ACI>B into two equal parts. QED PROP. XXXV.— THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to each other. (References— Prop. I 4, 29, 34 ; ax. 1, 3, 6.) Let the parallelograms ABCD, EBCF, be...

## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...two equal parts. Wherefore, the opposite aides &c. QED PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms A BCD, EBCF be on the same base BC, and between the sameparallels AF,BC: the parallelogram...

## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...two equal parts. Wherefore, the opposite sides &c. QED PROPOSITION 35. THEOREM. Parallelograms on 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 sameparallels AF, BC : the parallelogram...

## Annual Report

1868 - 886 pages
...triangle be produced, the exterior nngle is greater than cither of the interior opposite angles 15 i 2. Triangles upon the same base, and between the same parallels, are equal to one another 15 3. In any right -angled triangle, the square \rhieh is described upon the side subtending the right...

## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...Therefore, parallelograms upon equal, &c. QEJO. PROPOSITION XXXVII. THEOREM. Triangles upon the tame base and between the same parallels, are equal to one another. Let the triangles ABC, DBCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle ABC shall be...

## Linear Drawing: Showing the Application of Practical Geometry to Trade and ...

Ellis A. Davidson - Mechanical drawing - 1869 - 140 pages
...not necessarily be of the same shape to be of equal area, and by Euclid* (Book I., prop, xxxvii.), " Triangles upon the same base, and between the same parallels, are equal." If, therefore, lines be drawn from ABCDE and F to G, five triangles will be formed, having the same...

## Modern Methods in Elementary Geometry

E. M. Reynolds - Geometry - 1868 - 172 pages
...the parallelogram A CBF. Then ACBF = DBCE. But ABC is half of ACBF; therefore of DBCE. THEOREM IV. Triangles upon the same base and between the same parallels are equal. For each is half of any parallelogram on that base and between those parallels. COR. 1. Triangles upon...