| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...triangles upon the same base, &c. Which was to be demonstrated. PROPOSITION XXXVIII. THEOREM. — Triangles **upon equal bases, and between the same parallels, are equal to one another. Let** the triangles ABC, DEF be upon c ADH equal bases BC, EF, and between the same parallels AD, BF. The... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...4. The areas of all parallelograms, which have equal bases and heights, are equal to one another. 5. **Parallelograms upon equal bases, and between the same parallels, are equal to one another.** 6. The area of a parallelogram is found by multiplying the basis given in rods, feet, inches, &c.,... | |
| Euclid - 1835 - 540 pages
...equal to the triangle d 7. Ax. DBC. Wherefore, " triangles," &c. QED PROP. XXXVIII. THEOR. 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 : The triangle... | |
| Mathematics - 1835 - 684 pages
...the same base and altitude. PROP. 27. (Eue. i. 37, 38, 39, & 40.) Triangles upon the same base, or **upon equal bases, and between the same parallels, are equal to one another** : and conversely, equal triangles, upon the same base, or upon equal bases in the same straight line,... | |
| Mathematics - 1836 - 488 pages
...Parallelograms upon the same base and between the same parallels, are equal to one another. XXXVI. **Parallelograms upon equal bases, and between the same parallels, are equal to one another.** XXXVII. Triangles upon, the same base, and between the same parallels, are equal to one another. XXXVIII.... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...parallelogram AC is equal to the parallelogram BF.* Therefore parallelograms, &c. PROP. XXXVI. THEOR. **PARALLELOGRAMS upon equal bases, and between the same parallels, are equal to one another. Let** AC, EG be parallelograms upon equal bases BC, FG, and between the same parallels AH, BG; the parallelogram... | |
| Andrew Bell, Robert Simson - Euclid's Elements - 1837 - 290 pages
...7) ; therefore the triangle ABC is equal to the triangle DBC. PROPOSITION XXXVm. 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 ; the triangle... | |
| Robert Simson - Geometry - 1838 - 434 pages
...is, the he parallelogram EBCF. Therebase, &c. Q,. ED See the 2d and 3d figures. D PROP. XXXVI. THEOR. **PARALLELOGRAMS upon equal bases, and between the same...parallels, are equal to one another. Let ABCD, EFGH be** pa- A rallelograms upon equal bases BC, FG, and between the same parallels AH, BG; the parallelogram... | |
| Euclides - 1838 - 264 pages
...that cannot be suppressed, because it helps to prove the general case. PROP. XXXVIII. THEOR. Triangles **upon equal bases, and between the same parallels, are equal to one another. Let** the triangles ABC, DEF be upon eqnal bases BC EF, and between the same parallels BF, AD : the triangle... | |
| Euclid - Geometry - 1838 - 470 pages
...triangle ABC is equal to the triangle DBC. Wherefore triangles, &c. QED PROP. XXXVIII. THEOR. TRIANGLES **upon equal bases, and between the same parallels, are equal to one another.** BOOK I. THE ELEMENTS OF EUCLID. B E between the same parallels BF, AD : the triangle ABC is equal to... | |
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