 | Euclides - 1826 - 226 pages
...shall the two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted upon the same base, and between the same parallels, are equal to one another. » 3i. i. parallel to сл, " and through c draw CF, parallel to в D. Therefore each of them EBCA,... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...diameter BC divides the parallelogram ACDB into two equal parts.' ei. ED PROP. XXXV. THEOR. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parnllelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC : the... | |
 | John Playfair - Geometry - 1829 - 210 pages
...to each other. Therefore, parallelograms &c. QED ED. PROPOSITION XXXVII. THEOREM, Triangles on the same base, and between the same parallels, are equal to one another; that is, their surfaces are equal. Let the triangles ABC, DBC be on the same base BC, and between the... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...parallelograms upon equal bases, &c. Which was to be demonstrated. PROPOSITION XXXVII. THEOREM. — Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DEC be upon the same base BC, and between the same paral- EADF lels AD, BC. The... | |
 | Euclid - 1835 - 540 pages
...the parallelogram ABCD is equal to EFGH. Wherefore, " pa" rallelograms," &c. QED PROP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DEC be upon the same base BC, and between the same parallels AD, BC : The triangle... | |
 | Mathematics - 1835 - 684 pages
...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 parallels AF, В... | |
 | Mathematics - 1836 - 488 pages
...Parallelograms upon equal bases, and between the same parallels, are equal to one another. XXXVII. Triangles upon, the same base, and between the same parallels, are equal to one another. XXXVIII. Triangles upon equal bases, and between the same parallels, are equal to one another. XXXIX.... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...parallelogram ABCD is equal to EFGH. W||crefore, parallelograms, &c. QED XXXVII. THEOJl. Triangles ufon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels, AD, BC : The triangle... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...; and by the same ART. CGHD is also equal to CABD. Hence, EABF is equal to CGHD. This, &c. ART. 25. Triangles upon the same base and between the same parallels are equal. on the same base AC, and between —-77 the same parallels AC, DF. Then these triangles are equal.... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...the parallelogram AC is equal (I. ax. 1.) to EG. Wherefore parallelograms, &c. PROP. XXXVII. THEOR.* TRIANGLES upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, BC ; ABC is equal... | |
| |
Triangles upon the same base, and between the same parallels, are equal to one another. 
