 | Francis Wayland - Philosophy - 1861 - 444 pages
...that the triangles are equal ; REASONING. 303 Then, that a parallelogram and a triangle being on the same base and between the same parallels, the parallelogram is double of the triangle ; Hence, the triangles being equal, the parallelogram and the square must be equal. And, hence, the... | |
 | Francis Wayland - Philosophy - 1854 - 436 pages
...I first show that the triangles are equal ; Then, that a parallelogram and a triangle being on the same base and between the same parallels, the parallelogram is double of the triangle ; Hence, the triangles being equal, the parallelogram and the square must be equal. And, hence, the... | |
 | Euclides - 1855 - 270 pages
...then rest on the absurdity of the lesa triangU being equal to the greater. • D PROP. XLI. THEOREM. If a parallelogram and a triangle be upon the same...parallelogram is double of the triangle. Let the parallelogram BD, and the triangle EB С be upon the same base B С, and between the same parallels B С, A B. The... | |
 | John Playfair - Geometry - 1855 - 334 pages
...parallel to it but AD; AD is therefore parallel to BF. tv.ri'ii l!n- ssd^bp.-trallrls. PROP. XLI. THEOR. If a parallelogram and a triangle be upon the same base, and between tht same parallel; the parallelogram is double of the triangle. Let the parallelogram ABCD and the... | |
 | William Pease - 1856 - 108 pages
...the rectangle, and its perpendicular equal to a side of the rectangle adjacent to the base. REASON: "If a parallelogram and a triangle be upon the same...parallels, the parallelogram is double of the triangle." (Euclid, Book I. Prop. 41.) But, in these cases, the base of the triangles is double of that of the... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...side; and likewise the two interior angles upon the same side together equal to two right angles. 6. If a parallelogram and a triangle be upon the same...and between the same parallels : the parallelogram shall be double of the triangle. 7. If a straight line be divided into any two parts, the squares of... | |
 | 1856 - 428 pages
...being equal to the greater. PROPOSITION XLI. THEOREM. îf a parallelogram and a triangle b» upon tht same base, and between the same parallels; the parallelogram is double of the triangle, In fig. 41, let the parallelogram в D, and the triangle в в о be upon the same base в с, and... | |
 | Euclides - 1858 - 248 pages
...DEMONSTRATION. — P. 38. Triangles upon equal bases and between the same parallels are equal to one another. P. 41. If a parallelogram and a triangle be upon the...and between the same parallels, the parallelogram shall be double of the triangle. Ax. 6. The doubles of the same or of equal magnitudes are equal. ExP.... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...half a parallelogram upon the same base, and of equal altitude, or between the same parallels ; and " if a parallelogram and a triangle be upon the same...and between the same parallels, the parallelogram shall be double of the triangle." A trapezium is an irregular four-sided figure, of which the sides... | |
 | Euclides - 1868 - 88 pages
...DEM. 1 HC 3. 2 P. 38. 3 Hyp. 4 Ax. 1. 5 ex. als. 6 Concl. 7 Sim. 8 Concl. 9 Recap. PROP. XLI. THEOE. If a parallelogram and a triangle be upon the same base and between the same the parallelogram shall be double of the triangle. CON. Pst. 1. DEM. P. 37. 34. LTgr,. BIP 1 Eyp. 1.... | |
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If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle. 
