 | Geography - 1867 - 964 pages
...proceed to show. The reader will remember that in Problem XXIV (page 308) it was shown that triangles on the same base and between the same parallels are equal to one another, and that triangles on equal bases and between the same parallels are also equal to one... | |
 | Charles Hutton - Mathematics - 1812 - 620 pages
...BC, and also parallel ioit(th. 12). q. ED THEOREM XXV. PARALLELOGRAMS, as also Triangles, standing on the Same Base, and between the Same Parallels, are equal to each other. Let E Let ABCD, ABEP, be two parallelograms, and ABC, ABF, two triangles, standing on the same base... | |
 | Charles Hutton - Arithmetic - 1818 - 646 pages
...also parallel to it (lit. 12). .1. 1 . D. THEOREM XXV. . PARALLELOGRAMS, as also Triangles, standing on the Same Base, and between the Same Parallels, are equal to each ether. Let Let ABCD, ABEF, be two parallelo- 3> CF 3S grams, and ABC, ABF, two triangles, standing... | |
 | William Hawney - Geometry - 1820 - 336 pages
...of the wedge be perpendicular to its base ABFB, or inclined as ABI, since parallelopipedons standing on the same base and between the same parallels are equal to each other (Euclid, XI. and 29.) But when the edge CD of the wedge is longer or shorter than the base, by any... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...BC, and also parallel to it (th. 12). 4. ED THEOREM XXV. PARALLELOGRAMS, as also Triangles, standing on the Same Base, and between the Same Parallels, are equal to each other. Let £98 Let ABCD, ABEF, be two parallelograms, and ABC, ABF, two triangles, standing on the same base... | |
 | John Playfair - Geometry - 1829 - 210 pages
...are equal to each other. Therefore, parallelograms &c. QED ED. PROPOSITION XXXVII. THEOREM, Triangles on the same base, and between the same parallels, are equal to one another; that is, their surfaces are equal. Let the triangles ABC, DBC be on the same base BC,... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...whole Z ^BD = whole Z DCA, 4. that A ABC = A BCD. PROPOSITION XXXV. Theorem. Parallelograms upon the same 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, (Jigs.... | |
 | Charles Reiner - Geometry - 1837 - 246 pages
...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 parallelograms... | |
 | Chambers W. and R., ltd - 1842 - 744 pages
...feet coutaiiied in the table, namely, 16. It is demonstrated by Euclid, that parallelograms upon the same base and between the same parallels are equal to each other ; from this it follows that the area of a rhombus and a rhomboid can be ascertained by the same easy... | |
 | Education - 1843 - 582 pages
...right 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.... | |
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Parallelograms on the same base, and between the same parallels, are equal to one another. 
