| 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 of the... | |
| Euclid, Rev. John Allen - Astronomy - 1822 - 494 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 - 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
...C. PROPOSITION XL. THEOREM. (173) Equal triangles (BAC and EDF) on equal bases and on the same side, **are between the same parallels. For if the right line AD which joins the vertices of the** two triangles be not parallel to BF, draw through ^ the point A the right line AG parallel to BF, /(~~~"... | |
| Walter Henry Burton - Astronomy - 1828 - 68 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, James Thomson - Geometry - 1837 - 390 pages
...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
...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... | |
| 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,... | |
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