| Euclides - 1821 - 294 σελίδες
...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 of the... | |
| Euclid - 1822 - 222 σελίδες
...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....parallel to BC, draw through the point A a right line AF parallel to BC, cutting a side BD of the triangle BDC, or the side produced, in a point E different... | |
| Rev. John Allen - 1822 - 516 σελίδες
...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 - 1824 - 572 σελίδες
...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... | |
| Walter Henry Burton - 1828 - 84 σελίδες
...equal triangles Prop. xii. upon the same base (or upon equal bases in the same straight line) and upon the same side of it, are between the same parallels. For if the straight line which joins the vertices of the two triangles be not parallel to the base, some other... | |
| Euclid - 1833 - 216 σελίδες
...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 - 1833 - 168 σελίδες
...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, James Thomson - 1837 - 410 σελίδες
...angles (I. def. 38.) supplemental, the triangles are equal. PROB. XXXIX. THEOR.* EQUAL triangles upon the same 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... | |
| Euclides - 1840 - 82 σελίδες
...equal bases and between the same parallels, are equal. BDE PROP. XXXIX. THEOR. Equal triangles upon the same base and on the same side of it, 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,... | |
| Euclides - 1840 - 192 σελίδες
...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 that... | |
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