 | Mathematics - 1835 - 684 pages
...former, there remains (ax. 3.) the complement AE equal to E C. Therefore, &c. PROP. 24. (Eue. i. 35.) Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, E В С F, be upon the same base BG and between the same... | |
 | Mathematics - 1836 - 488 pages
...equal to one another, and the diameter bisects it, that is, divides it into two equal parts. XXXV. Parallelograms upon the same base and between the same parallels, are equal to one another. XXXVI. Parallelograms upon equal bases, and between the same parallels, are equal to... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...and Z CAB = BDC, 3. that whole Z ^BD = whole Z DCA, 4. that A ABC = A BCD. PROPOSITION XXXV. Theorem. Parallelograms upon the same base, and between the same parallels, are equal to each other. (In Jig. 1, the ams are equal, because each is double of A BDC.) Steps of the Demonstration,... | |
 | Charles Reiner - Geometry - 1837 - 254 pages
...likewise—what ? P.—The same perpendicular height; they have the same altitude. M.—And, since parallelograms upon the same base and between the same parallels are equal to each other, what may be inferred of equal parallelograms which are upon the same base ? P.—Equal... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...construction here given, however, it is so useful, that the student should be early acquainted with it. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF (figs. 2. and 3.) be upon the same base BC, and between... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the same straight line, they are between the same parallels. (1. 33, Cor.) PBOPOSITION XXXV. THEOREM. 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... | |
 | Thomas Holliday - Surveying - 1838 - 404 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.... | |
 | Euclides - 1838 - 264 pages
...BCD, and the diameter BC divides the parallelogram ACDB into two equal parts. QKD PROP. 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 base BC, and between the same parallels... | |
 | Euclides - 1840 - 82 pages
...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.... | |
 | Euclides - Geometry - 1841 - 378 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 same parallels, are equal to one another. Let the parallelograms ABCD, DBCF be upon the See the same base BC, and between the... | |
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Parallelograms upon the same base and between the same parallels, are equal to one another. 
