 | Euclides - 1821 - 294 pages
...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... | |
 | Rev. John Allen - Astronomy - 1822 - 516 pages
...1], are also equal [Ax. 7]. PROP. XXXIX. THEOR. Equal triangles (ABC, DBC), on the same base (BC), and on the same side of it, are between the same parallels. Join AD, which is parallel to BC ; for, if not, through A, draw AE parallel to BC[31. 1], meeting either... | |
 | Euclid - 1822 - 222 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 - 572 pages
...the same side of it, are between the same 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 - 542 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... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...to be demonstrated. 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... | |
 | Euclid - Euclid's Elements - 1833 - 216 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... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...AD is therefore parallel to it. Wherefore equal triangles, &c. PROP. XL. THEOR. EQUAL triangles upon equal bases, in the same straight line, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DEF, be upon equal bases BC, EF, in the same straight line BF, and on... | |
 | Euclides - 1840 - 192 pages
...parallel 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 - 82 pages
...are 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,... | |
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Equal triangles, on equal bases, in the same straight line, and on the same side of it, are between the same parallels. Let... 
