 | Euclides - 1855 - 270 pages
...two letters only which are at the vertices of any two of its opposite angles. PROP. XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms AС, B Г be upon the same base B С, and and between the same... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...Emmanuel College. WILLIAM HENRY BESAHT, MA St John's College. TUESDAY, January 6, 1857. 9... 12. 1. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. ABC is an isosceles triangle, of which A is the vertex : AB, AC, are bisected in D... | |
 | Euclides - 1856 - 168 pages
...the triangle BCD; therefore, the diameter BC divides the parallelogram into two equal parts. XXXVII. Parallelograms upon the same base and between the same parallels are equal to one another. Let the parallelograms ABCD, EBCF (Fig. 29) be upon the same base BC, and between the... | |
 | 1856 - 376 pages
...angles at the other side of the base are equal. ce, te anges at te oter se of te base are equa. 2. Parallelograms upon the same base and between the same parallels are equal. 3. To a given straight line to apply a parallelogram which shall be equal to a given triangle, ve one... | |
 | William Pease - 1856 - 108 pages
...opposite the base, to meet these perpendiculars, and the required rectangle will be formed. REASON : " Parallelograms, upon the same base, and between the same parallels," are equal to each other. (Euclid, Book I. Prop. 35.) PROBLEM LXX. To make a rectangle, one of its sides being... | |
 | W F. Richards - Elementary school teaching - 1856 - 198 pages
...are equal, and if the equal sides be produced, the angles at the other side of the base are equal. 2. Parallelograms upon the same base and between the same parallels are equal. 3. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and... | |
 | William E. Bell - Bridge building - 1857 - 250 pages
...Theorem. Parallelograms having equal bases and equal altitudes, contain equal areas, or are equivalent. Let the two parallelograms, ABCD and ABEF, have the same base, AB, and the same altitude PS ; then they will be equivalent. In the triangles BCB and ADF, the A ° * •ides... | |
 | William Whewell - Knowledge, Theory of - 1858 - 412 pages
...contingent truths. The former kind are Truths which cannot but be true; as that 19 and n make 30 ; — that parallelograms upon the same base and between the same parallels are equal; — that all the angles in the same segment of a circle are equal. The latter are Truths which it happens... | |
 | Euclides - 1858 - 248 pages
...four-sided figures of which the opposite sides are parallel ; . . BGHA & BPKD are parallelograms. ix. Parallelograms upon the same base and between the same parallels, are equal : x. EBAF and BGHA are parallelograms on the same base, &c. ; .'. EBAF and BGHA are equal parallelograms.... | |
 | War office - 1858 - 578 pages
...triangle be produced, the exterior angle is greater than either of the interior opposite angles. 2. Parallelograms upon the same base and between the same parallels are equal to one another. VOLUNTARY PORTION. 1. The opposite angles of a quadrilateral figure, inscribed in a... | |
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Parallelograms upon the same base and between the same parallels, are equal to one another. 
