| Euclides - 1821
...the given triangles as halves they are .-. equal, PROP. 39, THEOR. Equal triangles on the same base **and on the same side of it are between the same parallels,** For if they are not, draw through the vertex of one of them a line par. to the base, it cuts a side... | |
| Euclid - 1822 - 179 pages
...therefore equal(4). (' " . PROP. XXXIX. THEOR. Equal triangles (BAC and BDC) on the same base Fig-ss. **and on the same side of it are between the same parallels.** For if the right line AD which joins the vertices of the triangles be not parallel to BC, draw through... | |
| Edward Riddle - Nautical astronomy - 1824 - 551 pages
...parallele, Cor. 2. Equal triangles, or equal parallelograms on equal bases, in the same straight line **and on the same side of it are between the same parallels.** THEOREM XXXVII. If any two parallelograms, AC, EG, have two sides AB, AD, and the contained angle BAD... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...many equal parts. PROPOSITION XXXIX. THEOREM. (172) Equal triangles (BAG and BDC) on the same base **and on the same side of it are between the same parallels.** For if the right line AD which joins the vertices of the triangles be not parallel to BC, draw through... | |
| Euclid - Euclid's Elements - 1833 - 183 pages
...therefore _ * equal (4). PROP. XXXIX. THEOR. Equal triangles (BAC and BDC), on the same base Fig. 58. **and on the same side of it, are between the same parallels.** If the right line AD, which joins the vertices of the triangles, be not parallel to BC, draw through... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...PROPOSITION XL. See Note. THEOREM. — Equal triangles, upon equal bases in ihe same straight line, **and on the same side of it, are between the same parallels.** Let the triangles ABC, EFD, which are upon equal bases BC and EF in the same straight line BF, and... | |
| John Playfair - Geometry - 1837 - 318 pages
...ABC is equal to the triangle DEF. PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon **the same side of it, are between the same parallels. Join AD** ; AD is parallel to BC ; for, if it is not, through the point A draw (31. K) AE parallel to BC, and... | |
| Euclid, James Thomson - Geometry - 1837 - 390 pages
...base, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be **on the same base BC, and on the same side of it** ; they are between the same parallels. Join AD ; AD is parallel to BC. For, if it be not, through A... | |
| Euclides - 1840
...to AB. PROP. XL. THEOR. Equal triangles (ACB, DFE) on equal bases (AB, DE), in the same right line, **and on the same side of it, are between the same parallels.** For if it be supposed that CF joining the vertices of the equal triangles is not parallel to AE, but... | |
| Euclides - 1840
...between the same parallels. PROP. XL. THEOR. Equal triangles on equal bases, in the same right line, **and on the same side of it, are between the same parallels.** PROP. XLI. THEOR. If a parallelogram and a triangle are upon the same base and between the same parallels,... | |
| |