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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Σελίδα 35
των John Playfair - 1837 - 318 σελίδες
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 σελίδες
...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...

Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...therefore, also, the parallelogram ABCD is equal or equivalent to EFG н. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. TRIANGLES upon the same base, and between the same parallels, are equivalent to one another. Let the triangles ABC, DBC be upon the same base BC* and between the same...

Chambers's Information for the People, Τόμος 2

William Chambers, Robert Chambers - 1842
...to each other ; in proposition 37, the same fact is affirmed with respect to triangles, namely, that triangles upon the same base and between the same parallels, are equal. Propositions 36 and 38 are the converse of the preceding. The most celebrated, however, of the succeeding...

General Report on Public Instruction in the Bengal Presidency

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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1844 - 317 σελίδες
...to one another. triangle ABC is equal to the trian- E _ A ~D _ F gle DEC. Let the triangles ABC, DEC be upon the same base BC, and between the same parallels, AD, BC : The Produce AD both ways to the points E, F, and through B draw (31. 1.) BE parallel to CA ; and through...

The British Annals of Education for ...: Being The Scholastic ..., Τόμος 1

1844
...MODERATOR AND SENIOR EXAMINER. [The Differential Calculut it not to be wed.] 1 . Parallelograms on the same base and between the same parallels are equal to one another. 2. From a given circle to cut off a segment containing an angle equal to a given rectilineal angle....

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...divides the parallelogram ACDB 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 ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC. Then the...

Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 σελίδες
...ACDB into two equal parts. QED BOOK I. PROP. XXXV. XXXVI. PROPOSITION XXXV. THEOR. — Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same See the 2nd base BC, and between the same parallels AF,...

The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 σελίδες
...parallelogram AC is equal (I. ax. 1) to EG. Wherefore parallelograms, &c. PROP. XXXVII. TnEOR.t — Triangles upon the same base, and between the same parallels, are equal to one another. * lt will appear, from this proposition, that the perimeters of two equal parallelograms on the same...

A course of practical geometry for mechanics

William Pease - 1846
...form the isosceles triangle required. The reason of this is (Prob. XXXVII. Bk. I. Euclid,) because triangles upon the same base, and between the same parallels, are equal to one another : ie the triangles ACB and AE B, being upon the base, AB, to which the line EC is parallel, therefore...




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