 | Euclides - 1858 - 248 pages
...the opposite sides are parallel, and the diagonal joins opposite angles. DEMONSTRATION. — P. 35. Parallelograms on the same base and between the same parallels are equal. P. 34. The opposite sides and angles of parallelograms are equal, and the diameter bisects them. Ax.... | |
 | Anthony Nesbit - Measurement - 1859 - 494 pages
...equal to the parallelogram DBCE. (Euc.1.35. Simp.I1.2. Em.IH.6.) PAKT I. THEOREM VI. Triangles standing on the same base, and between the same parallels are equal to each other. Let the triangles ABC, DEC be upon the same base BC, and between /' \/ the same parallels... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...to one another. State and explain Euclid's Corollary to this proposition. 2. Parallelograms upon the same base and between the same parallels are equal to one another. VOLUNTARY PORTION. 1. About a given circle describe a triangle, equiangular to a given triangle. Given... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...1.) Therefore, parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. T•iangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, D-BCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle... | |
 | Henry William Watson, Edward John Routh - Mathematics - 1860 - 240 pages
...contained by AB and CD, the rect. AB, CD. 1. DEFINE parallel straight lines. Parallelograms upon the same base, and between the same parallels, are equal to one another. If a straight line DME be drawn through the middle point M of the base BC of a triangle ABC, so as... | |
 | William Whewell - Philosophy - 1860 - 604 pages
...with the first twenty-rix propositions of Euclid, and not till then, it becomes evident to him, that parallelograms on the same base and between the same parallels are equal ; and he cannot even conceive the contrary. When he has a little further cultivated his geometrical... | |
 | Henry William Watson, Edward John Routh - Mathematics - 1860 - 240 pages
...contained by AB and CD, the rect. AB, CD. 1. DEFINE parallel straight lines. Parallelograms upon the same base, and between the same parallels, are equal to one another. If a straight line DME be drawn through the middle point M of the base BC of a triangle ABC, so as... | |
 | Royal college of surgeons of England - 1860 - 332 pages
...angles equal to each other, these two straight lines shall be parallel. 5. Parallelograms upon the same base and between the same parallels are equal to one another. The perimeter of a square is less than that of any other parallelogram of equal area. 6. If a straight... | |
 | Euclides - 1860 - 288 pages
...therefore (Ax. 1) 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. Given the triangles ABC and DEC upon the same base BC, and between the same parallels AD and BC ; to... | |
 | Euclides - 1861 - 464 pages
...intervenes ; 5, to divide a / — 7 into two eq. pts. from a • in one of the sides, &c. 35. 113. Parallelograms on the same base and between the same parallels are equal, or rather equivalent, to one another. SCH. — The equality of / 7s proved by the Method of Indivisibles.... | |
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Triangles upon the same base, and between the same parallels, are equal to one another. 
