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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 ... - Σελίδα 111
των Thomas Perronet Thompson - 1833 - 150 σελίδες
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Principles of geometry, mensuration, trigonometry, land-surveying, and ...

Thomas Tate (mathematical master.) - 1848 - 284 σελίδες
...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 σελίδες
...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 Advancement of Science, Τόμος 48

American Association for the Advancement of Science - 1899 - 648 σελίδες
...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, Τόμοι 1-6

582 σελίδες
...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 - 382 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1853 - 400 σελίδες
...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...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 σελίδες
...divides the parallelogram a С db into two equal parts. QED PROPOSITION XXXV. — THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. LET the parallelograms abСd, ebСf (see the second figure) be upon the same base b С, andbetween the same...

The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 σελίδες
...diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOREM. 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...




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