 | John Playfair - 1842 - 332 σελίδες
...adjacent angles of a parallelogram is equal to two right angles. 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... | |
 | Euclides - 1842 - 316 σελίδες
...therefore, also, the parallelogram ABCD is equal or equivalent to EFG н. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. TRIANGLES upon the same base, and between the same parallels, are equivalent to one another. Let the triangles ABC, DBC be upon the same base BC* and between the same... | |
 | William Chambers, Robert Chambers - 1842 - 938 σελίδες
...to each other ; in proposition 37, the same fact is affirmed with respect to triangles, namely, that triangles upon the same base and between the same parallels, are equal. Propositions 36 and 38 are the converse of the preceding. The most celebrated, however, of the succeeding... | |
 | 1843 - 582 σελίδες
...angles, or are together equal to two right angles. 2. Define a parallelogram. Parallelograms on the same base and between the same parallels are equal to one another. Shew that if any quadrilateral figure be bisected by both its diagonals it is a parallelogram. 3. To... | |
 | John Playfair - 1844 - 338 σελίδες
...to one another. triangle ABC is equal to the trian- E _ A ~D _ F gle DEC. Let the triangles ABC, DEC be upon the same base BC, and between the same parallels, AD, BC : The Produce AD both ways to the points E, F, and through B draw (31. 1.) BE parallel to CA ; and through... | |
 | 1844 - 688 σελίδες
...MODERATOR AND SENIOR EXAMINER. [The Differential Calculut it not to be wed.] 1 . Parallelograms on the same base and between the same parallels are equal to one another. 2. From a given circle to cut off a segment containing an angle equal to a given rectilineal angle.... | |
 | Euclides - 1845 - 546 σελίδες
...divides the parallelogram ACDB into two equal parts. QED PROPOSITION XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC. Then the... | |
 | Euclid - 1845 - 218 σελίδες
...ACDB into two equal parts. QED BOOK I. PROP. XXXV. XXXVI. PROPOSITION XXXV. THEOR. — Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same See the 2nd base BC, and between the same parallels AF,... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...parallelogram AC is equal (I. ax. 1) to EG. Wherefore parallelograms, &c. PROP. XXXVII. TnEOR.t — Triangles upon the same base, and between the same parallels, are equal to one another. * lt will appear, from this proposition, that the perimeters of two equal parallelograms on the same... | |
 | W. PEASE - 1846 - 86 σελίδες
...form the isosceles triangle required. The reason of this is (Prob. XXXVII. Bk. I. Euclid,) because triangles upon the same base, and between the same parallels, are equal to one another : ie the triangles ACB and AE B, being upon the base, AB, to which the line EC is parallel, therefore... | |
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Parallelograms upon the same base and between the same parallels, are equal to one another. 
