 | Great Britain. Committee on Education - 1848
...extent of Palestine, and what was its population in the time of David? GEOMETRY.— (Inverness.) 1. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram is double of the trianslc. 2. The sum of the squares of the diameters... | |
 | Euclides - 1848
...same straight line, and towards the same parts, are between the same parallels. PROP. XLI. THEOREM. If a parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram shall be double of the triangle. PROP. XLII. PROBLEM. To describe a parallelogram... | |
 | Great Britain. Council on Education - 1848
...diameters of any parallelogram is equal to the sum of the squares of the sides of the parallelogram. 1. If a parallelogram and a triangle be upon the same base, and betweerf the same parallels, the parallelogram is double of the triansle. 3. In a circle, the angle... | |
 | Euclides - 1853
...but AD; therefore 4. AD is parallel to BF. Wherefore, equal triangles, &c. aED PROP. XLI. THEOREM. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle... | |
 | Euclid, John Playfair - 1853 - 317 pagina’s
...that there is no other parallel to it bul AD ; AD is therefore parallel to BF. , / ' PROP. XLfTTHEOR. If a parallelogram and a triangle be upon the same base, and betioeen the same parallel ; the parallelogram is double of the triangle. D Let the parallelogram ABCD... | |
 | Euclides - 1855
...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 base, and between the same parallels ; the parallelogram is double of the triangle. Let the parallelogram BD, and the triangle... | |
 | John Playfair - 1855 - 318 pagina’s
...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... | |
 | Cambridge univ, exam. papers - 1856
...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 base, and between the same parallels : the parallelogram shall be double of the triangle. 7. If a straight line be divided into... | |
 | William Pease - 1856
...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 base, and between the same parallels, the parallelogram is double of the triangle." (Euclid, Book I. Prop. 41.) But, in these... | |
 | Euclides - 1858
...each two sides and their included angle equal, the triangles are in every other respect equal. P. 41. If a parallelogram and a triangle be upon the same base and between the same parallels, the parallelogram is double of the triangle. Ax. 6. Things double of the same are equal... | |
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If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle. 
