 | Euclides - 1837 - 112 σελίδες
...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,... | |
 | Robert Simson - 1838 - 434 σελίδες
...PROP. XXXVII. THEOR. TRIANGLES upin the same base, and between the same parallels, are equal to bne another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, E AD F BC : the triangle ABCjs equal to the triangle DBC. Produce AD both witys to the points E, F,... | |
 | Euclides - 1838 - 264 σελίδες
...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 AF, BC : the parallelogram... | |
 | Thomas Holliday - 1838 - 404 σελίδες
...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... | |
 | Euclides - 1840 - 82 σελίδες
...XXXVI. THEOR. Parallelograms on equal bases and between the. same parallels, are equal. DG _H a )•: PROP. XXXVII. THEOR. Triangles upon the same base and between the same parallels, are equal. BC__DP PROP. XXXVIII. THEOR. Triangles upon equal bases and between the same parallels, are equal.... | |
 | Euclides - 1841 - 378 σελίδες
...the same EBCH: therefore the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. Triangles upon the same base,...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... | |
 | 1862 - 556 σελίδες
...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... | |
 | Euclides - 1842 - 316 σελίδες
...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... | |
 | John Playfair - 1842 - 332 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... | |
 | William Chambers, Robert Chambers - 1842 - 938 σελίδες
...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... | |
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Parallelograms upon the same base and between the same parallels, are equal to one another. 
