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

## Principles of geometry, mensuration, trigonometry, land-surveying, and ...

Thomas Tate (mathematical master.) - 1848 - 284 pages
...ADGK = the parallelogram ADCB; therefore the triangle ADF is also = half the parallelogram ADCB. Cor. Triangles upon the same base and between the same parallels are equal. Application of this Theorem. 1. To show that the rectangle BCGF _—^— A o contains double the surface...

## The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. Parallelograms upon the same base and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF (see the 2d and 3d figures) be upon the same base BC, and between the same...

## Proceedings of the American Association for the ..., Volume 48, Part 1899

American Association for the Advancement of Science - 1899 - 648 pages
...third part a strict treatment of equivalence. Even Euclid, in proving his I. 35, "Parallelograms on the same base, and between the same parallels, are equal to one another," does not show that the parallelograms can be divided into pairs of pieces admitting of superposition...

## Papers for the schoolmaster, Volumes 1-6

582 pages
...possess in being situated as they are. EUCLID AND MECHANICS. First Year Student*. 1. Parallelograms upon the same base and between the same parallels are equal to one another, 2. If a straight line be divided into any two parts, the squares of the whol« line, and of one of...

## Annual Report of the Commissioners ...

1851
...Prove that the three angles of a triangle are equal to two right angles, .... — 10 3 2. Prove that triangles, upon the same base, and between the same parallels, are equal, 12 1 3. Describe a square upon a given straight line, . 11 2 4. Divide a given straight line in medial...

## The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852 - 152 pages
...the sake of practice, be proved with the accompanying figure.] AB PROP. XXXV. THEOK. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC ; the parallelogram...

## The Elements of Euclid [book 1] for beginners, by J. Lowres

Euclides - 1852 - 48 pages
...35.) ; therefore the parallelograms ABCD and EFGH are equal (Ax. 1.). WWD РBОР. XXXVП. ТнЕОB. Triangles upon the same base and between the same parallels are equal. Let the triangles в A c and в D c be on the same base в c, and between the same parallels в c and...

## The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...BC divides the parallellogram ACDB into two equal parts. QED PROPOSITION XXXV. THEOR. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, KBCF be upon the same base BC, and between the same parallels AF; BC : the parallelogram...