 | Euclides - 1868 - 88 pages
...HC 4 P. 33. 5 Def. A. 6 D. 5. H. 7 P. 35. 8 P. 85. 9 Ax. 1. 10 Becap. • PilOP. XXXVII. Тикоа. Triangles upon the same base and between the same parallels are equal to one ano CON. Pst. 2. P. 31. Def. A. DEM. P. 35. 34. Ax. 7. SCHOL. PIIOP. XXXVIII. TIIEOU. Triangles upon... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...shall be greater than the base of the other. 2. Define a parallelogram ; prove that parallelograms upon the same base and between the same parallels are equal to one another. 3. If a straight line be divided into any two parts, the squares of the whole line and of one of the... | |
 | Euclides - 1860 - 288 pages
...is equal to the same parallelogram EBCH ; therefore (Ax. 1) the parallelogram ABCD is equal to EFGH. PROPOSITION XXXVII. THEOREM. Triangles upon the same...between the same parallels, are equal to one another. Given the triangles ABC and DEC upon the same base BC, and between the same parallels AD and BC ; to... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...-BCdivides the parallelogram A CDB 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 AB CD, EBCF be upon the same base 2? C, and between the same parallels AF, BC. Then... | |
 | Royal college of surgeons of England - 1860 - 336 pages
...triangle are greater than the third. Show that the difference of any two sides is less than the third. 5. Triangles upon the same base and between the same parallels are equal to one another. 6. If the square described upon one of the sides of a triangle be equal to the squares described upon... | |
 | Henry William Watson, Edward John Routh - Mathematics - 1860 - 240 pages
...rectangle contained by AB and CD, the rect. AB, CD. 1. DEFINE parallel straight lines. Parallelograms upon the same base, and between the same parallels, are equal to one another. If a straight line DME be drawn through the middle point M of the base BC of a triangle ABC, so as... | |
 | John Playfair - Geometry - 1860 - 332 pages
...same EBCH : Therefore also the parallelogram ABOI? it «qual to EFGH. PROP. XXXVII. THEOR. Trim gles upon the same base, and between the same parallels, are equal to ont another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels, AD,... | |
 | War office - 1861 - 260 pages
...less than — — . MATHEMATICS. REV. CANON HEAVISIDE, MA Voluntary Paper, No. II. 1. Parallelograms upon the same base and between the same parallels are equal to one another. 2. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained... | |
 | Euclides - 1862 - 140 pages
...parallelogram EFGH. (ax. 1.) Conclusion. — Therefore, parallelograms, &c. QED PROPOSITION 37.— THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. (References— Prop. I. 31, 34, 35; ax. 7.) Hypothesis. — Let the triangles ABC, DBC, be on the same... | |
 | Euclides - 1862 - 172 pages
...is equal to the triangle BCD ; (l. 4) 44 THE SCHOOL EUCLID. PROP. XXXV.— THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to each other. (References— Prop. i. 4, 29, 34 ; ax. 1, 3, 6.) Let the parallelograms ABCD, EBCF, be... | |
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Parallelograms upon the same base and between the same parallels, are equal to one another. 
