| Euclides - 1862 - 172 pages
...parallelogram E3CT. Therefore, parallelograms upon the same base, &c. QED PROP. XXXVI.— THEOREM. **Parallelograms upon equal bases and between the same parallels are equal to one another.** (References — Prop. i. 33, 34, 35; ax. 1.) Let ABCD, EFGH be parallelograms upon equal bases BC,... | |
| Euclides - 1862 - 140 pages
...the triangle DBC. Conclusion. — Therefore, triangles, &c, QED PROPOSITION 38.— THEOREM. Triangles **upon equal bases, and between the same parallels, are equal to one another.** (References— Prop. I. 31, 34, 36; ax. 7.) Hypothesis. — Let the triangles ABC, DEF, be on equal... | |
| Euclides - 1863 - 74 pages
...units, or uiiits of surface in the parallelogram. PROP. 36.— THEOR.— (A Corollary of the 35th). **Parallelograms upon equal bases, and between the same parallels, are equal to one another.** , CON.— Pst. 1.— DEM.— P. 34, Ax. 1, P. 33, Def. A, P. 35 Hyp. 1. Let the / — 7s ABCD, EFGH,... | |
| University of Oxford - Education, Higher - 1863 - 316 pages
...given point in a given straight line, make a rectilineal angle equal to a given rectilineal angle. 5. **Parallelograms upon equal bases, and between the same parallels, are equal to one another.** 6. Describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given... | |
| Robert Potts - 1863 - 482 pages
...of an isosceles triangle be produced, the angles upon the other side of the base shall be equal. 9. **Parallelograms upon equal bases and between the same parallels are equal to one another.** A parallelogram has one side fixed, while the other sides move in such a manner that its area is- always... | |
| Architecture - 1863 - 300 pages
...sides ; also by a line drawn perpendicular to one of the sides. 8. Proposition 38, Theorem ; Triangles **upon equal bases and between the same parallels are equal to one another.** 9. Divide an equilateral trianglo into four equal triangles. Book 2. 10. Proposition 7, Theorem ; It... | |
| Euclides - 1864 - 262 pages
...the parallelogram-E.BCF. Therefore, parallelograms upon the same, &c. QED PROPOSITION XXXVI. THEOREM. **Parallelograms upon equal bases and between the same parallels, are equal to one another. Let ABCD,** EFGIfbe parallelograms upon equal bases BC, FG, and between the same parallels AH, BG. Then the parallelogram... | |
| Woolwich roy. military acad - 1864 - 588 pages
...Find the present value of 1L due 12 years hence, when money bears 4^ per cent, compound interest. 9. **Parallelograms upon equal bases and between the same parallels are equal to one another.** other circle be described with centre C, chords of this latter which, produced if necessary, pa&s through... | |
| Euclides - 1864 - 448 pages
...is equal to the triangle DBC. Wherefore, triangles, &c. QED PROPOSITION XXXVIII. 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 the... | |
| University of Cambridge - 1864 - 694 pages
...AB iť " sq. on AB," and for the rectangle contained by AB and CO, " the rect. AB, CD." 1. TRIANGLES **upon equal bases and between the same parallels are equal to one another.** If a quadrilateral figure have two sides parallel, and the parallel sides be bisected, the line joining... | |
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