| 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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