 | Walter Henry Burton - 1828 - Liczba stron: 84
...ix. jj_ The next proposition is very important, and the truth of it is not obvious at first sight. Parallelograms on the same base, and between the same parallels, are equal. A.. I perceive that it is so in your first figure, where the diagonal of one parallelogram serves for... | |
 | John Playfair - 1829 - Liczba stron: 210
...nor solids. LUDLAM. Hence we can find the area of any parallelogram, or of any plane triangle. All parallelograms on the same base and between the same parallels are equal (35. 1.), whether they be right or oblique angled. Let a and b denote the number of feet (or any other... | |
 | Pierce Morton - 1830 - Liczba stron: 584
...a rectangle of the same base and altitude. PROP. 25. (Eue. i. 36.) Parallelograms upon equal bases, and between the same parallels, are equal to one another. Let the parallelogramsABCD, E FGH, be upon equal bases BC, FG, and between the same parallels AH, BG. The parallelogram... | |
 | Thomas Perronet Thompson - 1833 - Liczba stron: 168
...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 - 1833 - Liczba stron: 304
...other, as being together with these equal angles = to two right angles (prop. 29.) PROP. 35, THEOR. Parallelograms on the same base and between the same parallels are equal. Connect the sides opposite the base, (if necessary,) then there are two triangles formed (viz. the... | |
 | Euclides - 1834 - Liczba stron: 518
...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... | |
 | 1835 - Liczba stron: 684
...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 С ; the parallelogram ABCD... | |
 | Euclid - 1835 - Liczba stron: 540
...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... | |
 | Alexander Smith - 1835 - Liczba stron: 350
...the mathematicians teach us that the three angles of a triangle are equal to two right angles ; that parallelograms on the same base, and between the same parallels, are equal, and the like ; and they likewise teach us why this is true ; ie they shew how these truths necessarily... | |
 | Alexander Smith (M.A.) - 1835 - Liczba stron: 750
...the mathematicians teach us that the three angles of a triangle are equal to two right angles ; that parallelograms on the same base, and between the same parallels, are equal, and the like ; and they likewise teach us why this is true ; ie they shew how these truths necessarily... | |
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Triangles upon the same base, and between the same parallels, are equal to one another. 
