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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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - Geometry - 1838 - 416 pages
...BCD, and the diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. PARALLELOGRAMS upon the same base, and between the...to one another.* Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC ; the parallelogram ABCD shall be equal...
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A complete treatise on Practical Land-Surveying, etc

Thomas Holliday - Surveying - 1838 - 80 pages
...quadrilateral figure be equal, they will alto be parallel, and the figure will be a parallelogram. 3. Parallelograms upon the same base and between the same parallels are equal to one another. 4. A parallelogram is double the area of a triangle of the same base and altitude. See fig. 22, plate...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...rectangle AB • BC to the rectangle DE • EF. Draw AG, DH perpendicular to BC, EF respectively. Because parallelograms upon the same base and between the same parallels are equal, the parallelogram AC is equal to the rectangle AG-BC and the parallelogram DF to the rectangle DH-EF....
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...parallelogram are equal, and it is bisected or divided into two equal parts by a diagonal. PROP. XXXV. THEOR. Parallelograms upon the same base and between the same parallels are equal. c ED p PROP. XXXVI. THEOR. Parallelograms on equal bases and between the. same parallels, are equal....
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels, are equal to one another. BC, and between the same parallels AD, BC: the triangle ABC shall be equal to the triangle DBC. Produce...
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Punch, Volumes 42-43

Caricatures and cartoons - 1862
...Nasty pig you are. You learn those ways at school, and nothing else. Master Bob. Don't I, Miss. Hee ! Parallelograms upon the same base and between the same parallels are equal to 9ne another, and equal triangles upon equal bases in the same straight lines, and towards the same...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...sum of any two adjacent angles of a parallelogram is equal to two right angles. PROP. XXXV. THEOR. Parallelograms upon the same base and between the same parallels, are equal to one another. (SEE THE 2d AND 3d FIGUREs.) Let the parallelograms ABCD, EBCF be upon the same base BC, and between...
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Chambers's information for the people, ed. by W. and R. Chambers, Volume 2

Chambers W. and R., ltd - 1842
...whole number of square feet coutaiiied in the table, namely, 16. It is demonstrated by Euclid, that parallelograms upon the same base and between the same parallels are equal to each other ; from this it follows that the area of a rhombus and a rhomboid can be ascertained by the...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...BCD, and the diameter вc divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. PARALLELOGRAMS upon the same base, and between the same parallels, are equal or equivalent to one another. Let the parallelograms ABCD, EBCF be upon the same base вc, and between...
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General Report on Public Instruction in the Bengal Presidency

Education - 1843
...angles, or are together equal to two right angles. 2. Define a parallelogram. Parallelograms on the same base and between the same parallels are equal to one another. Shew that if any quadrilateral figure be bisected by both its diagonals it is a parallelogram. 3. To...
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