| Thomas Fowler - 1870 - 348 sider
...which our deductive reasoning proceeds. The proposition proved in Euclid, Book i. Prop. 38, that ' **Triangles upon equal bases, and between the same parallels, are equal to one another,'** is derived from, or is the total result of, the previous deductions (i) that ' Parallelograms upon... | |
| Henry William Watson - 1871 - 285 sider
...of the triangle ABC is equal to the area of the triangle DBC (Bk. IV. Prop. i, Cor.). PROPOSITION 7. **Triangles upon equal bases and between the same parallels are equal to one another** in area. Let ABC and DEF be two triangles upon the equal bases BC and EF, and between the same parallels... | |
| Euclides - 1871
...parallel straight lines, and the lines AD, BC intersect in E, then the triangles AEC, BED are equal. **Triangles upon equal bases, and between the same parallels, are equal to one another.** Let AS ABC, DEF be on equal bases, BC, EF and between the same IIs BF, AD. Then must A ABC= A DEF.... | |
| Edinburgh univ - 1871
...5, and 2 doors, each 9 feet by four, with paper I £ yards wide, at 5jd. a yard. 4. Parallelograms **upon equal bases and between the same parallels are equal to one another.** Prove this ; and modify the enunciation, so as to extend it to the case where the parallelograms are... | |
| Euclides, James Hamblin Smith - 1872 - 349 sider
...straight lines, and the lines AD, BC intersect in E, then the triangles AEC, BED are equal. PROPOSITION **XXXVIII. THEOREM. Triangles upon equal bases, and...between the same parallels, are equal to one another.** Let AS A BO, DEF be on equal bases, BC, EF and between the same Us BF, AD. Then must &ABC= &DEF. From... | |
| Popular educator - 1872
...a to any point in the straight line HE, produced both ways indefinitely. Triangles also which stand **upon equal bases and between the same parallels are equal to one another.** Thus, the triangles t, H o, M ot, which B _ stand on equal c bases, H o, ro, and H _ L.-'' P "-..MK... | |
| Henry Major - 1873
...diameter AB bisects it ; and DEC is the half of DBCF ; therefore ABC is equal to DEC. XXXVIII. — **Triangles upon equal bases, and between the same parallels, are equal to one another.** Let the triangles ABC, DEF, be upon equal bases BC, EF, and between the same parallels BF, AD. Produce... | |
| Euclides - 1874
...5. The triangle ABC is equal to the triangle DBC. Wherefore, triangles, &c. QED PROPOSITION 38. — **Theorem. Triangles upon equal bases and between the same parallels, are equal to one another.** Let the triangles ABC, DEF be upon' equal bases BC, EF, and between the same parallels BF, AD. Then... | |
| Edward Atkins - 1874
...the triangle ABC is equal to the triangle DBC. Therefore, triangles, &c. Q. E, D. Proposition 38. — **Theorem, Triangles upon equal bases, and between the same parallels, are equal to one another.** Let the triangles ABC, DEF, be on equal bases BC, EF, and between the same parallels BF, AD. The triangle... | |
| Braithwaite Arnett - 1874
...consecutive angles of a quadrilateral is half the sum of the two remaining angles. 2. Parallelograms -on **equal bases, and between the same parallels, are equal to one another.** 3. Divide a given straight line into two parts, so that the rectangle contained by the whole and one... | |
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