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" DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. "
Elements of geometry, with ... trigonometry - Page 106
by André Darré - 1872
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pages
...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...
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The First Six Books with Notes

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...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

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...
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...which D С is a 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...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

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...
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The First Six Books of the Elements of Euclid: With Notes

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...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...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...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

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,...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...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...
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