 | Walter Henry Burton - 1828 - 84 pagina’s
...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 - 210 pagina’s
...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 - 584 pagina’s
...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 - 168 pagina’s
...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 - 304 pagina’s
...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 - 518 pagina’s
...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 - 684 pagina’s
...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 - 540 pagina’s
...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 - 350 pagina’s
...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 - 750 pagina’s
...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. 
