 | Augustus De Morgan - 1831 - 108 pages
...BGHA and BPKD are four- sided figures &c. (Construction.) .-. BGHA and BPKD are parallelograms. IX. Parallelograms upon the same base and between the same parallels are equal. (Proved.) EBAFandBGHA, are parallelograms &c. (Construction.) .•. EBAF and BGHA are equal. X. Parallelograms... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...the diameter BC divides the parallelogram ACDB into two equal parts. Therefore, &c. QED 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... | |
 | 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 triangle... | |
 | Euclides - 1834 - 518 pages
...equal parts. QED PROPOSITION XXXV. THBOR. — Parallelograms upon t he same base, and between See N, the same parallels, are equal to one another. Let...the parallelograms ABCD, EBCF be upon the same base See the 2d BC, and between the same parallels AF, BC : the parallelo- and sd figram ABCD shall be equal... | |
 | 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...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 С ; the parallelogram ABCD... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...two equal parts. QED c.4. 1. PROP. XXXV. THEOR. Parallelograms upon the same base, and between See N. the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same See the base BC, and between the same parallels AF, BC; the paral- *fdand 3d lelogram ABCD is equal... | |
 | Euclid - 1835 - 540 pages
...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 ABC... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...also, the sum of any two adjacent angles of a parallelogram-is equal to two right angles. PROP. XXIX. THEOR. Parallelograms upon the same base and between the same parallels, are equivalent to one another. (sEE THE 2d AND 3d FIGUREs.) Let the parallelograms ABCD, EBCF be upon the... | |
 | 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 one another. XXXVII.... | |
 | 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... | |
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Parallelograms upon the same base, and between the same parallels, are equal to one another. 
