| 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 the... | |
| 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 - 544 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 the... | |
| Walter Henry Burton - Astronomy - 1828 - 84 pages
...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 - 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... | |
| Euclid - 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... | |
| Euclides - 1840 - 82 pages
...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 - 194 pages
...therefore be also greater than Z. BDC, of which however it is but a part ; which is absurd. Therefore, two **triangles on the same base, and on the same side of it,** cannot have their conterminous sides equal at both extremities of the base, when the vertex of the... | |
| |