| Euclides - 1821 - 294 pages
...= parallelograms formed of which 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 - 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... | |
| 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... | |
| Edward Riddle - Nautical astronomy - 1824 - 572 pages
...part, can be parallel to AB, and DC is consequently parallel to A BQED Cor. 1. Equal parallelograms, on the same base, and on 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... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...triangle into as 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... | |
| Euclides - 1833 - 304 pages
...parallelograms formed, of which the given triangles are halves ; they are /. equal. PROP. 39, THEOR. Eg ual 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... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 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... | |
| 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... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...to the triangle CDE (V. 9). And they are on the same base DE ; but equal triangles on the same base are between the same parallels (I. 39) ; therefore DE is parallel to BC. PROPOSITION III. THEOREM. hare the same ratio which the other sides of the triangle have to one another... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...a point in which the circumferences meet, the circles must touch one another in that point. IF two triangles on the same base, and on the same side of it, have equal vertical angles, the vertex of each is in the circumference of the circle described about... | |
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