 | 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... | |
 | 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... | |
 | Mathematics - 1836 - 352 pages
...BGHA and Í3 PKD 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.) EB AF and BGH A, are parallelograms &c. (Construction.) .: EBAF and BGHA are equal. X. Parallelograms... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...AC = CD, DB each to each, and Z CAB = BDC, 3. that whole Z ^BD = whole Z DCA, 4. that A ABC = A BCD. PROPOSITION XXXV. Theorem. Parallelograms upon the...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,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...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 to... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...EBCH ; therefore also the parallelogram ABCD is equal to EFGH. PROPOSITION XXXVII. THEOREM. 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 ; the triangle ABO... | |
 | Charles Reiner - Geometry - 1837 - 254 pages
...likewise—what ? P.—The same perpendicular height; they have the same altitude. M.—And, since parallelograms upon the same base and between the same parallels are equal to each other, what may be inferred of equal parallelograms which are upon the same base ? P.—Equal... | |
 | Charles Reiner - Geometry - 1837 - 246 pages
...are about the diagonal of a square are, likewise, squares. 6. Parallelograms and triangles which are upon the same base and between the same parallels are equal to each other. 7. Parallelograms and triangles which are upon equal bases and between the same parallels... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...BCD, and the diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. PARALLELOGRAMS upon the same base, and between the...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 ABCD... | |
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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
